Quantum Physics
- [1] arXiv:2406.03509 [pdf, ps, html, other]
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Title: Coherent states of the asymmetric harmonic oscillatorComments: 13 pages, 13 figuresSubjects: Quantum Physics (quant-ph)
We constructed formal coherent states for an asymmetric harmonic oscillator, where the asymmetry parameter is the square root of the ratio of spring constants. Although these states are constructed based on both Glauber's and Perelomov's approaches, in general they do not satisfy all the properties required for coherent states. Over time, the coherent states introduced in this way generally become incoherent. However, there are some specific parameters for the square root ratios of the spring constants $\frac{4k+1}{4l+1}$ or $\frac{4k+3}{4l+3}$. For these parameters it is possible to construct coherent states on the subspace of the Hilbert space of eigenstates. These coherent states keep their coherence during the time evolution. This case is also analyzed.
- [2] arXiv:2406.03531 [pdf, ps, html, other]
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Title: Mixed-Dimensional Qudit State Preparation Using Edge-Weighted Decision DiagramsComments: 6 pages, 4 figures, 1 tableJournal-ref: Design Automation Conference 2024, San Francisco (USA)Subjects: Quantum Physics (quant-ph)
Quantum computers have the potential to solve important problems which are fundamentally intractable on a classical computer. The underlying physics of quantum computing platforms supports using multi-valued logic, which promises a boost in performance over the prevailing two-level logic. One key element to exploiting this potential is the capability to efficiently prepare quantum states for multi-valued, or qudit, systems. Due to the time sensitivity of quantum computers, the circuits to prepare the required states have to be as short as possible. In this paper, we investigate quantum state preparation with a focus on mixed-dimensional systems, where the individual qudits may have different dimensionalities. The proposed approach automatically realizes quantum circuits constructing a corresponding mixed-dimensional quantum state. To this end, decision diagrams are used as a compact representation of the quantum state to be realized. We further incorporate the ability to approximate the quantum state to enable a finely controlled trade-off between accuracy, memory complexity, and number of operations in the circuit. Empirical evaluations demonstrate the effectiveness of the proposed approach in facilitating fast and scalable quantum state preparation, with performance directly linked to the size of the decision diagram. The implementation is freely available as part of Munich Quantum Toolkit~(MQT), under the framework MQT Qudits at this http URL.
- [3] arXiv:2406.03546 [pdf, ps, html, other]
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Title: Entanglement Asymmetry in non-Abelian Anyonic SystemsComments: 5+9 pages, 1+10 figures, comments are welcome!Subjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th)
Non-Abelian anyons, a promising platform for fault-tolerant topological quantum computation, adhere to the charge super-selection rule (cSSR), which imposes restrictions on physically allowed states and operations. However, the ramifications of cSSR and fusion rules in anyonic quantum information theory remain largely unexplored. In this study, we unveil that the information-theoretic characteristics of anyons diverge fundamentally from those of non-anyonic systems such as qudits, bosons, and fermions and display intricate structures. In bipartite anyonic systems, pure states may have different marginal spectra, and mixed states may contain pure marginal states. More striking is that in a pure entangled state, parties may lack equal access to entanglement. This entanglement asymmetry is manifested in quantum teleportation employing an entangled anyonic state shared between Alice and Bob, where Alice can perfectly teleport unknown quantum information to Bob, but Bob lacks this capability. These traits challenge conventional understanding, necessitating new approaches to characterize quantum information and correlations in anyons. We expect that these distinctive features will also be present in non-Abelian lattice gauge field theories. Our findings significantly advance the understanding of the information-theoretic aspects of anyons and may lead to realizations of quantum communication and cryptographic protocols where one party holds sway over the other.
- [4] arXiv:2406.03595 [pdf, ps, other]
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Title: Overlap integral of stationary scattering statesComments: arXiv admin note: text overlap with arXiv:2305.16939Subjects: Quantum Physics (quant-ph)
The overlap integrals of scattering states in potentials of finite widths are expressed with their asymptotic behaviors and those of energies $E_1$ and $E_2$ consist of diagonal terms that are proportional to $\delta(E_1-E_2)$ and nondiagonal terms. Owing to the composition of nondiagonal terms, superpositions of stationary states have time-dependent norms and finite probability currents. These do not represent isolate states. In various exceptional potentials and in free theory, nondiagonal terms do not exist, and the superpositions of states with different energies represent isolate particles that exactly describe scattering processes.
- [5] arXiv:2406.03627 [pdf, ps, html, other]
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Title: Optimal Control and Glassiness in Quantum SensingSubjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Atomic Physics (physics.atom-ph)
Quantum systems are powerful detectors with wide-ranging applications from scanning probe microscopy of materials to biomedical imaging. Nitrogen vacancy (NV) centers in diamond, for instance, can be operated as qubits for sensing of magnetic field, temperature, or related signals. By well-designed application of pulse sequences, experiments can filter this signal from environmental noise, allowing extremely sensitive measurements with single NV centers. Recently, optimal control has been used to further improve sensitivity by modification of the pulse sequence, most notably by optimal placement of $\pi$ pulses. Here we consider extending beyond $\pi$ pulses, exploring optimization of a continuous, time-dependent control field. We show that the difficulty of optimizing these protocols can be mapped to the difficulty of finding minimum free energy in a classical frustrated spin system. While most optimizations we consider show autocorrelations of the sensing protocol that grow as a power law -- similar to an Ising spin glass -- the continuous control shows slower logarithmic growth, suggestive of a harder Heisenberg-like glassy landscape.
- [6] arXiv:2406.03748 [pdf, ps, html, other]
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Title: Avoiding Barren Plateaus with EntanglementComments: 15 pages, 9 figuresSubjects: Quantum Physics (quant-ph)
In the search for quantum advantage with near-term quantum devices, navigating the optimization landscape is significantly hampered by the barren plateaus phenomenon. This study presents a strategy to overcome this obstacle without changing the quantum circuit architecture. We propose incorporating auxiliary control qubits to shift the circuit from a unitary $2$-design to a unitary $1$-design, mitigating the prevalence of barren plateaus. We then remove these auxiliary qubits to return to the original circuit structure while preserving the unitary $1$-design properties. Our experiment suggests that the proposed structure effectively mitigates the barren plateaus phenomenon. A significant experimental finding is that the gradient of $\theta_{1,1}$, the first parameter in the quantum circuit, displays a broader distribution as the number of qubits and layers increases. This suggests a higher probability of obtaining effective gradients. This stability is critical for the efficient training of quantum circuits, especially for larger and more complex systems. The results of this study represent a significant advance in the optimization of quantum circuits and offer a promising avenue for the scalable and practical implementation of quantum computing technologies. This approach opens up new opportunities in quantum learning and other applications that require robust quantum computing power.
- [7] arXiv:2406.03770 [pdf, ps, html, other]
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Title: Wave packet dynamics of entangled q-deformed statesComments: 8 pages, 5 figuresSubjects: Quantum Physics (quant-ph)
This paper explores the wave packet dynamics of a math-type q- deformed field interacting with atoms in a Kerr-type nonlinear medium. The primary focus is on the generation and dynamics of entanglement using the q- deformed field, with the quantification of entanglement accomplished through the von Neumann entropy. Two distinct initial q-deformed states, the q-deformed Fock state, and the q-deformed coherent state, are investigated. The entanglement dynamics reveal characteristics of periodic, quasi-periodic, and chaotic behavior. Non-deformed initial states display wave packet near revivals and fractional revivals in entanglement dynamics while introducing q-deformation eliminates these features. The q-deformation significantly influences wave packet revivals and fractional revivals, with even a slight introduction causing their disappearance. For large values of q, the entanglement dynamics exhibit a chaotic nature. In the case of a beam splitter-type interaction applied to the initial deformed Fock state, an optimal deformation parameter q is identified, leading to maximum entanglement exceeding the non-deformed scenario.
- [8] arXiv:2406.03775 [pdf, ps, html, other]
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Title: Nonstandard derivation of the Gorini-Kossakowski-Sudarshan-Lindblad master equation of a quantum dynamical semigroup from the Kraus representationComments: 16 pagesSubjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)
We give a new nonstandard proof of a well-known theorem that the generator $L$ of a quantum dynamical semigroup $\exp(tL)$ on a finite-dimensional quantum system has a specific form called a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generator (also known as a Lindbladian) and vice versa. The proof starts from the Kraus representation of the quantum channel $\exp (\delta t L)$ for an infinitesimal hyperreal number $\delta t>0$ and then estimates the orders of the traceless components of the Kraus operators. The jump operators then naturally arise as the standard parts of the traceless parts divided by $\sqrt{\delta t}$. We also give a nonstandard proof of a related fact that close completely positive maps have close Kraus operators.
- [9] arXiv:2406.03781 [pdf, ps, html, other]
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Title: Operator dynamics and entanglement in space-time dual Hadamard latticesSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Exactly Solvable and Integrable Systems (nlin.SI)
Many-body quantum dynamics defined on a spatial lattice and in discrete time -- either as stroboscopic Floquet systems or quantum circuits -- has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with $q$ states per site, defined on the square lattice by a complex partition function and paremeterized in terms of $q\times q$ Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata [J. Math. Phys. 49, 112104 (2008)] and in the $q\to\infty$ limit to the classical spatiotemporal cat model of many body chaos [Nonlinearity 34, 2800 (2021)]. We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper [Phys. Rev. B 105, 144306 (2022)] can be reinterpreted in purely graphical terms and directly applied here.
- [10] arXiv:2406.03804 [pdf, ps, html, other]
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Title: Exploring the interplay between mass-energy equivalence, interactions and entanglement in an optical lattice clockAnjun Chu, Victor J. Martínez-Lahuerta, Maya Miklos, Kyungtae Kim, Peter Zoller, Klemens Hammerer, Jun Ye, Ana Maria ReyComments: 7+17 pages, 4+6 figuresSubjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); General Relativity and Quantum Cosmology (gr-qc); Atomic Physics (physics.atom-ph)
We propose protocols that probe manifestations of the mass-energy equivalence in an optical lattice clock (OLC) interrogated with spin coherent and entangled quantum states. To tune and uniquely distinguish the mass-energy equivalence effects (gravitational redshift and second order Doppler shift) in such setting, we devise a dressing protocol using an additional nuclear spin state. We then analyze the interplay between photon-mediated interactions and gravitational redshift and show that such interplay can lead to entanglement generation and frequency synchronization. In the regime where all atomic spins synchronize, we show the synchronization time depends on the initial entanglement of the state and can be used as a proxy of its metrological gain compared to a classical state. Our work opens new possibilities for exploring the effects of general relativity on quantum coherence and entanglement in OLC experiments.
- [11] arXiv:2406.03851 [pdf, ps, html, other]
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Title: Entanglement-assist cyclic weak-value-amplification metrologyComments: 12 pages, 8 figuresSubjects: Quantum Physics (quant-ph); Optics (physics.optics)
Weak measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and signal-to-noise ratio (SNR) of weak measurement from distinct perspectives. Here, we incorporate a power recycling cavity into the entanglement-assisted weak measurement system. We obtain an improvement of both detection efficiency and Fisher information, and find that the improvement from entanglement and recycling occur in different dimensions. Furthermore, we analyze two types of errors, walk-off errors and readout errors. The conclusions suggest that entanglement exacerbates the walk-off effect caused by recycling, but this detriment can be balanced by proper parameter selection. In addition, power-recycling can complement entanglement in suppressing readout noise, thus enhancing the accuracy in the measurement results and recovering the lost Fisher information. This work delves deeper into the metrological advantages of weak measurement.
- [12] arXiv:2406.03856 [pdf, ps, html, other]
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Title: Multidimensional Quantum Generative Modeling by Quantum Hartley TransformSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
We develop an approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions. First, we design a differentiable Hartley feature map parametrized by real-valued argument that enables quantum models suitable for solving stochastic differential equations and regression problems. Unlike the naturally complex Fourier encoding, the proposed Hartley feature map circuit leads to quantum states with real-valued amplitudes, introducing an inductive bias and natural regularization. Next, we propose a quantum Hartley transform circuit as a map between computational and Hartley basis. We apply the developed paradigm to generative modeling from solutions of stochastic differential equations, and utilize the quantum Hartley transform for fine sampling from parameterized distributions through an extended register. Finally, we present tools for implementing multivariate quantum generative modeling for both correlated and uncorrelated distributions. As a result, the developed quantum Hartley models offer a distinct quantum approach to generative AI at increasing scale.
- [13] arXiv:2406.03867 [pdf, ps, html, other]
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Title: A Comprehensive Study of Quantum Arithmetic CircuitsComments: Under review at the Royal Society's Philosophical Transactions ASubjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET)
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as a prominent illustration. Quantum arithmetic circuits, which are the fundamental building blocks in numerous quantum algorithms, have attracted much attention. Despite extensive exploration of various designs in the existing literature, researchers remain keen on developing novel designs and improving existing ones.
In this review article, we aim to provide a systematically organized and easily comprehensible overview of the current state-of-the-art in quantum arithmetic circuits. Specifically, this study covers fundamental operations such as addition, subtraction, multiplication, division and modular exponentiation. We delve into the detailed quantum implementations of these prominent designs and evaluate their efficiency considering various objectives. We also discuss potential applications of presented arithmetic circuits and suggest future research directions. - [14] arXiv:2406.03905 [pdf, ps, html, other]
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Title: QuAS: Quantum Application Score for benchmarking the utility of quantum computersComments: 9 pages, 5 figuresSubjects: Quantum Physics (quant-ph)
Benchmarking quantum computers helps to quantify them and bringing the technology to the market. Various application-level metrics exist to benchmark a quantum device at an application level. This paper presents a revised holistic scoring method called the Quantum Application Score (QuAS) incorporating strong points of previous metrics, such as QPack and the Q-score. We discuss how to integrate both and thereby obtain an application-level metric that better quantifies the practical utility of quantum computers. We evaluate the new metric on different hardware platforms such as D-Wave and IBM as well as quantum simulators of Quantum Inspire and Rigetti.
- [15] arXiv:2406.03906 [pdf, ps, html, other]
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Title: Megastable quantization in self-excited systemsComments: 5 pages, 3 figuresSubjects: Quantum Physics (quant-ph)
A classical particle in a confining potential gives rise to a Hamiltonian conservative dynamical system with an uncountably infinite continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite discrete energy levels. We consider a class of nonlinear self-sustained oscillators describing a classical active particle in a harmonic potential. These nonlinear oscillators emerge in the low-memory regime of both state-dependent time-delay systems as well as in non-Markovian stroboscopic models of walking droplets. Using averaging techniques, we prove the existence of a countably infinite number of asymptotically stable quantized orbits, i.e. megastability, for this class of self-excited systems. The set of periodic orbits consists of a sequence of nested limit-cycle attractors with quasilinear increasing amplitude and alternating stability, yielding smooth basins of attraction. By using the Lyapunov energy function, we estimate the energy spectra of this megastable set of orbits, and perform numerical simulations to confirm the mathematical analysis. Our formalism can be extended to self-excited particles in general confining potentials, resulting in different energy-frequency relations for these dynamical analogs of quantization.
- [16] arXiv:2406.03908 [pdf, ps, html, other]
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Title: Noisy certification of continuous variables graph statesSubjects: Quantum Physics (quant-ph)
Continuous variables (CV) offer a promising platform for the development of various applications, such as quantum communication, computing, and sensing, and CV graph states represent a family of powerful entangled resource states for all these areas. In many of these protocols, a crucial aspect is the certification of the quantum state subsequently used. While numerous protocols exist, most rely on assumptions unrealistic for physical continuous variable states, such as infinite precision in quadrature measurement or the use of states requiring infinite squeezing. In this work, we adapt existing protocols to deal with these unavoidable considerations, and use them to certify their application for different quantum information tasks. More specifically, we show how CV graph states can be efficiently verified and certified even in a noisy and imperfect setting. We then discuss how our findings impact the usability of states obtained after the protocol for different applications, including quantum teleportation, computing, and sensing.
- [17] arXiv:2406.03945 [pdf, ps, html, other]
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Title: Locally inaccessible hidden quantum correlationsComments: 9 pages, 4 figuresSubjects: Quantum Physics (quant-ph)
We prove, modulo a conjecture on quantum steering ellipsoids being true, the existence of the phenomenon of locally inaccessible hidden quantum correlations. That is, the existence of two-particle states whose hidden quantum correlations cannot be revealed by local filters implemented exclusively on one side of the experiment, but that can still be revealed when both parties cooperate in applying judiciously chosen local filters. The quantum correlations here considered are the violation of the CHSH-inequality for Bell-nonlocality and the violation of the $\rm F_3$-inequality for EPR-steering. Specifically, we provide a necessary criterion for guaranteeing the presence of such phenomenon for arbitrary two-qubit states. This criterion in turn relies on the conjecture that the maximal violation of CHSH-inequality and $\rm F_3$-inequality are both upper bounded by functions that depend on the magnitude of the quantum steering ellipsoid centre. This latter conjecture, although currently lacking an analytical proof, is supported by numerical results. We use this necessary criterion to explicitly show examples of two-qubit states with locally inaccessible hidden quantum correlations and, furthermore, two-qubit states with locally inaccessible maximal hidden quantum correlations.
- [18] arXiv:2406.03964 [pdf, ps, html, other]
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Title: Quantum Speed Limits for Implementation of Unitary TransformationsComments: 13 pagesSubjects: Quantum Physics (quant-ph)
Quantum speed limits are the boundaries that define how quickly one quantum state can transform into another. Instead of focusing on the transformation between pairs of states, we provide bounds on the speed limit of quantum evolution by unitary operators in arbitrary dimensions. These do not depend on the initial and final state but depend only on the trace of the unitary operator that is to be implemented and the gross characteristics (average and variance) of the energy spectrum of the Hamiltonian which generates this unitary evolution. The bounds that we find can be thought of as the generalization of the Mandelstam-Tamm (TM) and the Margolus-Levitin (MT) bound for state transformations to implementations of unitary operators. We will discuss the application of these bounds in several classes of transformations that are of interest in quantum information processing.
- [19] arXiv:2406.03972 [pdf, ps, html, other]
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Title: Eigenpath traversal by Poisson-distributed phase randomisationComments: 19 pagesSubjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS)
We present a framework for quantum computation, similar to Adiabatic Quantum Computation (AQC), that is based on the quantum Zeno effect. By performing randomised dephasing operations at intervals determined by a Poisson process, we are able to track the eigenspace associated to a particular eigenvalue.
We derive a simple differential equation for the fidelity, leading to general theorems bounding the time complexity of a whole class of algorithms. We also use eigenstate filtering to optimise the scaling of the complexity in the error tolerance $\epsilon$.
In many cases the bounds given by our general theorems are optimal, giving a time complexity of $O(1/\Delta_m)$ with $\Delta_m$ the minimum of the gap. This allows us to prove optimal results using very general features of problems, minimising the problem-specific insight necessary.
As two applications of our framework, we obtain optimal scaling for the Grover problem (i.e.\ $O(\sqrt{N})$ where $N$ is the database size) and the Quantum Linear System Problem (i.e.\ $O(\kappa\log(1/\epsilon))$ where $\kappa$ is the condition number and $\epsilon$ the error tolerance) by direct applications of our theorems. - [20] arXiv:2406.04004 [pdf, ps, html, other]
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Title: T-Count Optimizing Genetic Algorithm for Quantum State PreparationComments: To appear in IEEE QSW 2024 proceedingsSubjects: Quantum Physics (quant-ph); Neural and Evolutionary Computing (cs.NE)
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the number of qubits to be initialized grows, the circuits required to implement the desired state also exponentially increase in size leading to loss of fidelity to noise. This is mainly due to the susceptibility to environmental effects of the non-Clifford T gate, whose use should thus be reduced as much as possible. In this paper, we present and utilize a genetic algorithm for state preparation circuits consisting of gates from the Clifford + T gate set and optimize them in T-Count as to reduce the impact of noise. Whilst the method presented here does not always produce the most accurate circuits in terms of fidelity, it can generate high-fidelity, non-trivial quantum states such as quantum Fourier transform states. In addition, our algorithm does automatically generate fault tolerantly implementable solutions where the number of the most error prone components is reduced. We present an evaluation of the algorithm when trialed against preparing random, Poisson probability distribution, W, GHZ, and quantum Fourier transform states. We also experimentally demonstrate the scalability issues as qubit count increases, which highlights the need for further optimization of the search process.
- [21] arXiv:2406.04083 [pdf, ps, html, other]
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Title: Leakage Mobility in Superconducting Qubits as a Leakage Reduction UnitJoan Camps, Ophelia Crawford, György P. Gehér, Alexander V. Gramolin, Matthew P. Stafford, Mark TurnerComments: 6+4 pages, 3+4 figuresSubjects: Quantum Physics (quant-ph)
Leakage from the computational subspace is a damaging source of noise that degrades the performance of most qubit types. Unlike other types of noise, leakage cannot be overcome by standard quantum error correction techniques and requires dedicated leakage reduction units. In this work, we study the effects of leakage mobility between superconducting qubits on the performance of a quantum stability experiment, which is a benchmark for fault-tolerant logical computation. Using the Fujitsu Quantum Simulator, we perform full density-matrix simulations of stability experiments implemented on the surface code. We observe improved performance with increased mobility, suggesting leakage mobility can itself act as a leakage reduction unit by naturally moving leakage from data to auxiliary qubits, where it is removed upon reset. We compare the performance of standard error-correction circuits with "patch wiggling", a specific leakage reduction technique where data and auxiliary qubits alternate their roles in each round of error correction. We observe that patch wiggling becomes inefficient with increased leakage mobility, in contrast to the improved performance of standard circuits. These observations suggest that the damage of leakage can be overcome by stimulating leakage mobility between qubits without the need for a dedicated leakage reduction unit.
- [22] arXiv:2406.04114 [pdf, ps, html, other]
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Title: Harmonic generation with topological edge states and electron-electron interactionComments: 7 pages, 5 figuresSubjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Atomic Physics (physics.atom-ph); Optics (physics.optics)
It has been found previously that the presence or absence of topological edge states in the Su-Schrieffer-Heeger (SSH) model has a huge impact on harmonic generation spectra. More specifically, the yield of harmonics for harmonic orders that correspond to photon energies below the band gap is many orders of magnitude different in the trivial and topological phase. It is shown in this work that this effect is still present if electron-electron interaction is taken into account, i.e., if a Hubbard term is added to the SSH Hamiltonian. To that end, finite SSH-Hubbard chains at half filling are considered that are short enough to be accessible to exact diagonalization but already showing edge states in the topological phase. We show that the huge difference in the harmonic yield between the trivial and the topological phase can be reproduced with few-level models employing only the many-body ground state and a few excited many-body states.
- [23] arXiv:2406.04157 [pdf, ps, other]
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Title: Circuit-level fault tolerance of cat codesSubjects: Quantum Physics (quant-ph)
Bosonic codes offer the possibility of storing quantum information in a single infinite-dimensional physical system endowed with the capability to correct errors, thereby reducing the number of physical components needed to protect against noise. Much of the current efforts in bosonic codes are on correcting only loss errors, while deferring the correction of phase errors -- perhaps actively suppressed -- to subsequent layers of encoding with standard qubit codes. Rotationally symmetric bosonic codes, which include the well-known cat and binomial codes, are capable of simultaneous correction of both loss and phase errors, offer an alternate route that deals with arbitrary errors already at the base layer. Grimsmo et al. [PRX 10, 011058 (2020)] analyzed the family of such codes and proposed general error-correction circuits to correct both loss and phase errors, reporting high noise thresholds in the presence of loss and phase errors on the input, while the error-correction circuits remain noiseless. A proper assessment, however, requires consideration of circuit-level noise, where the individual circuit components can themselves be faulty and introduce errors on the encoded information. Here, we carry out such a circuit-level analysis, and assess the performance of the error-correction circuits for the storage of information encoded with cat codes. While the circuits of Grimsmo et al.~are formally fault tolerant even under circuit-level noise, the thresholds are significantly worse. We show how, through waiting-time optimization and the use of squeezing, we can restore the noise requirements to ones plausibly achievable with near-term quantum hardware. Our circuit-level analysis also reveals important features of the error-correction circuits not visible in the earlier ideal-circuit perspective.
- [24] arXiv:2406.04190 [pdf, ps, html, other]
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Title: Probing quantum complexity via universal saturation of stabilizer entropiesComments: 13 pages, 8 figuresSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
Nonstabilizerness or `magic' is a key resource for quantum computing and a necessary condition for quantum advantage. Non-Clifford operations turn stabilizer states into resourceful states, where the amount of nonstabilizerness is quantified by resource measures such as stabilizer Rényi entropies (SREs). Here, we show that SREs saturate their maximum value at a critical number of non-Clifford operations. Close to the critical point SREs show universal behavior. Remarkably, the derivative of the SRE crosses at the same point independent of the number of qubits and can be rescaled onto a single curve. We find that the critical point depends non-trivially on Rényi index $\alpha$. For random Clifford circuits doped with T-gates, the critical T-gate density scales independently of $\alpha$. In contrast, for random Hamiltonian evolution, the critical time scales linearly with qubit number for $\alpha>1$, while is a constant for $\alpha<1$. This highlights that $\alpha$-SREs reveal fundamentally different aspects of nonstabilizerness depending on $\alpha$: $\alpha$-SREs with $\alpha<1$ relate to Clifford simulation complexity, while $\alpha>1$ probe the distance to the closest stabilizer state and approximate state certification cost via Pauli measurements. As technical contributions, we observe that the Pauli spectrum of random evolution can be approximated by two highly concentrated peaks which allows us to compute its SRE. Further, we introduce a class of random evolution that can be expressed as random Clifford circuits and rotations, where we provide its exact SRE. Our results opens up new approaches to characterize the complexity of quantum systems.
- [25] arXiv:2406.04199 [pdf, ps, other]
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Title: High-Fidelity Electron Spin Gates in a Scalable Diamond Quantum RegisterTimo Joas, Florian Ferlemann, Roberto Sailer, Philipp J. Vetter, Jingfu Zhang, Ressa S. Said, Tokuyuki Teraji, Shinobu Onoda, Tommaso Calarco, Genko Genov, Matthias M. Müller, Fedor JelezkoSubjects: Quantum Physics (quant-ph)
Diamond is a promising platform for quantum information processing as it can host highly coherent qubits that might allow for the construction of large quantum registers. A prerequisite for such devices is a coherent interaction between electron nitrogen vacancy (NV) spins. Entanglement between dipolar-coupled NV spin pairs has been demonstrated, but with a limited entanglement fidelity and its error sources have not been characterized. Here, we design a robust, easy to implement entangling gate between NV spins in diamond and quantify the influence of multiple error sources on the gate performance. Experimentally, we demonstrate a record gate fidelity of $F=(96.0 \pm 2.5)$ % under ambient conditions. Our identification of the dominant errors paves the way towards NV-NV gates beyond the error correction threshold.
- [26] arXiv:2406.04217 [pdf, ps, html, other]
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Title: Optomechanical Backaction in the Bistable RegimeComments: 5 pages, 4 figuresSubjects: Quantum Physics (quant-ph)
With a variety of realisations, optomechanics utilizes its light matter interaction to test fundamental physics. By coupling the phonons of a mechanical resonator to the photons in a high quality cavity, control of increasingly macroscopic objects has become feasible. In such systems, state manipulation of the mechanical mode is achieved by driving the cavity. To be able to achieve high drive powers the system is typically designed such that it remains in a linear response regime when driven. A nonlinear response and especially bistability in a driven cavity is often considered detrimentally to cooling and state preparation in optomechanical systems and is avoided in experiments. Here we show, that with an intrinsic nonlinear cavity backaction cooling of a mechanical resonator is feasible operating deeply within the nonlinear regime of the cavity. With our theory taking the nonlinearity into account, precise predictions on backaction cooling can be achieved even with a cavity beyond the bifurcation point, where the cavity photon number spectrum starts to deviate from a typical Lorentzian shape.
- [27] arXiv:2406.04245 [pdf, ps, html, other]
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Title: Online learning of a panoply of quantum objectsComments: 34 pages. Comments welcomeSubjects: Quantum Physics (quant-ph); Machine Learning (cs.LG)
In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation metric for such a strategy is its regret, or roughly the accumulated errors in hypothesis statistics. We prove a sublinear regret bound for learning over general subsets of positive semidefinite matrices via the regularized-follow-the-leader algorithm and apply it to various settings where one wishes to learn quantum objects. For concrete applications, we present a sublinear regret bound for learning quantum states, effects, channels, interactive measurements, strategies, co-strategies, and the collection of inner products of pure states. Our bound applies to many other quantum objects with compact, convex representations. In proving our regret bound, we establish various matrix analysis results useful in quantum information theory. This includes a generalization of Pinsker's inequality for arbitrary positive semidefinite operators with possibly different traces, which may be of independent interest and applicable to more general classes of divergences.
- [28] arXiv:2406.04246 [pdf, ps, html, other]
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Title: Complementary polynomials in quantum signal processingComments: 24 pages, 4 figuresSubjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this problem employ numerical methods that are not amenable to explicit error analysis. We present a new approach to complementary polynomials using complex analysis. Our main mathematical result is a contour integral representation for a canonical complementary polynomial. The integral representation on the unit circle has a particularly simple and efficacious Fourier analytic interpretation, which we use to develop a Fast Fourier Transform-based algorithm for the efficient calculation of $Q$ in the monomial basis with explicit error guarantees. Numerical evidence that our algorithm outperforms the state-of-the-art optimization-based method for computing complementary polynomials is provided.
- [29] arXiv:2406.04250 [pdf, ps, html, other]
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Title: Online learning of quantum processesComments: 14 + 72 pages, 6 figuresSubjects: Quantum Physics (quant-ph); Machine Learning (cs.LG); Machine Learning (stat.ML)
Among recent insights into learning quantum states, online learning and shadow tomography procedures are notable for their ability to accurately predict expectation values even of adaptively chosen observables. In contrast to the state case, quantum process learning tasks with a similarly adaptive nature have received little attention. In this work, we investigate online learning tasks for quantum processes. Whereas online learning is infeasible for general quantum channels, we show that channels of bounded gate complexity as well as Pauli channels can be online learned in the regret and mistake-bounded models of online learning. In fact, we can online learn probabilistic mixtures of any exponentially large set of known channels. We also provide a provably sample-efficient shadow tomography procedure for Pauli channels. Our results extend beyond quantum channels to non-Markovian multi-time processes, with favorable regret and mistake bounds, as well as a shadow tomography procedure. We complement our online learning upper bounds with mistake as well as computational lower bounds. On the technical side, we make use of the multiplicative weights update algorithm, classical adaptive data analysis, and Bell sampling, as well as tools from the theory of quantum combs for multi-time quantum processes. Our work initiates a study of online learning for classes of quantum channels and, more generally, non-Markovian quantum processes. Given the importance of online learning for state shadow tomography, this may serve as a step towards quantum channel variants of adaptive shadow tomography.
- [30] arXiv:2406.04263 [pdf, ps, html, other]
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Title: No real advantage of photon subtraction and displacement in continuous variable measurement device independent quantum key distributionComments: Please also see the companion paper titled "Optimization of state parameters in displacement assisted photon subtracted measurement-device-independent quantum key distribution"Subjects: Quantum Physics (quant-ph)
We critically analyse the role of single photon subtraction (SPS) and displacement in improving the performance of continuous variable measurement device independent quantum key distribution (CV-MDI-QKD). We consider CV-MDI-QKD with resource states generated by SPS on a displaced two-mode squeezed vacuum state. Optimizing the secret key rate with state parameters reveals that implementing SPS yields no benefits in improving the loss tolerance of CV-MDI-QKD. Additionally, we find that displacement too is not useful in improving the performance of CV-MDI-QKD. While our result is in contradistinction with the widely held belief in the field regarding the utility of SPS and displacement in CV-MDI-QKD, it also calls for a re-examination of the role of non-Gaussian operations in increasing the efficiency of various quantum information processing protocols.
- [31] arXiv:2406.04270 [pdf, ps, html, other]
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Title: Optimization of state parameters in displacement assisted photon subtracted measurement-device-independent quantum key distributionComments: Please also see the companion paper titled "No real advantage of photon subtraction and displacement in continuous variable measurement device independent quantum key distribution"Subjects: Quantum Physics (quant-ph)
Non-Gaussian operations, in particular, photon subtraction (PS), have been shown to enhance the performance of various quantum information processing tasks including continuous variable measurement device independent quantum key distribution (CV-MDI-QKD). This work investigates the role of non-Gaussian resource states, namely, the photon subtracted two-mode squeezed coherent (PSTMSC) (which include photon subtracted two-mode squeezed vacuum (PSTMSV) as a special case) states in CV-MDI-QKD. To this end, we derive the Wigner characteristic function for the resource states, from which the covariance matrix and, finally, the secret key rate expressions are extracted. The optimization of the state parameters is undertaken to find the most suitable resource states in this family of states. There have been previous studies on the PSTMSV and PSTMSC states in CV-MDI-QKD that make use of PS operation. We evaluate such proposals and find to our surprise that both PSTMSC and PSTMSV resource states underperform as compared to the TMSV state rendering PS operation and displacement undesirable.
- [32] arXiv:2406.04272 [pdf, ps, html, other]
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Title: Entangling Quantum Memories at Channel CapacityComments: 14 pages; 8 figures; Comments are welcome!Subjects: Quantum Physics (quant-ph)
Entangling quantum memories, mediated by optical-frequency or microwave channels, at high rates and fidelities is key for linking qubits across short and long ranges. All well-known protocols encode up to one qubit per optical mode, hence entangling one pair of memory qubits per transmitted mode over the channel, with probability $\eta$, the channel's transmissivity. The rate is proportional to $\eta$ ideal Bell states (ebits) per mode. The quantum capacity, $C(\eta) = -\log_2(1-{\eta})$ ebits per mode, which $\approx 1.44\eta$ for high loss, i.e., $\eta \ll 1$, thereby making these schemes near rate-optimal. However, $C(\eta) \to \infty$ as $\eta \to 1$, making the known schemes highly rate-suboptimal for shorter ranges. We show that a cavity-assisted memory-photon interface can be used to entangle matter memories with Gottesman-Kitaev-Preskill (GKP) photonic qudits, which along with dual-homodyne entanglement swaps that retain analog information, enables entangling memories at capacity-approaching rates at low loss. We benefit from loss resilience of GKP qudits, and their ability to encode multiple qubits in one mode. Our memory-photon interface further supports the preparation of needed ancilla GKP qudits. We expect our result to spur research in low-loss high-cooperativity cavity-coupled qubits with high-efficiency optical coupling, and demonstrations of high-rate short-range quantum links.
- [33] arXiv:2406.04275 [pdf, ps, html, other]
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Title: Interfacing Gottesman-Kitaev-Preskill Qubits to Quantum MemoriesComments: 17 pages; 8 figures; Comments are welcome!Subjects: Quantum Physics (quant-ph)
Gottesman-Kitaev-Preskill (GKP) states have been demonstrated to pose significant advantages when utilized for fault-tolerant all optical continuous-variable quantum computing as well as for quantum communications links for entanglement distribution. However interfacing these systems to long-lived solid-state quantum memories has remained an open problem. Here we propose an interface between quantum memories and GKP qubit states based on a cavity-mediated controlled displacement gate. We characterize the quality of memory-GKP entanglement as a function of cavity parameters suggesting optimal regimes of operation for high-quality state transfer between either qubit states. We further extend this protocol to demonstrate the creation of GKP cluster states by avoiding the requirement of ancillary optical quadrature-squeezed light. Utilizing post-selected entanglement swapping operations for GKP qubits, we demonstrate the utility of our protocol for high-rate entanglement generation between quantum memories. Extensions and derivatives of our proposal could enable a wide variety of applications by utilizing the operational trade-offs for qubits encoded in memory and in the GKP basis.
- [34] arXiv:2406.04285 [pdf, ps, html, other]
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Title: Robust preparation of ground state phases under noisy imaginary time evolutionComments: 13 pages, 7 figuresSubjects: Quantum Physics (quant-ph)
Non-unitary state preparation protocols such as imaginary time evolution (ITE) offer substantial advantages relative to unitary ones, including the ability to prepare certain long-range correlated states more efficiently. Here, we ask whether such protocols are also robust to noise arising due to coupling to the environment. We consider a non-unitary ITE "circuit" subjected to a variety of noise models and investigate whether the resulting steady state remains in the same phase as the target state of the ITE at finite noise strength. Taking the one-dimensional quantum Ising model as a concrete example, we find that the ground state order and associated phase transition persist in the presence of noise, provided the noise does not explicitly break the symmetry that protects the phase transition. That is, the noise must possess the protecting symmetry in a weak (or average) form. Our analysis is facilitated by a mapping to an effective Hamiltonian picture in a doubled Hilbert space. We discuss possible implications of these findings for quantum simulation on noisy quantum hardware.
- [35] arXiv:2406.04305 [pdf, ps, html, other]
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Title: Quixer: A Quantum Transformer ModelComments: 17 pages, 8 figuresSubjects: Quantum Physics (quant-ph)
Progress in the realisation of reliable large-scale quantum computers has motivated research into the design of quantum machine learning models. We present Quixer: a novel quantum transformer model which utilises the Linear Combination of Unitaries and Quantum Singular Value Transform primitives as building blocks. Quixer operates by preparing a superposition of tokens and applying a trainable non-linear transformation to this mix. We present the first results for a quantum transformer model applied to a practical language modelling task, obtaining results competitive with an equivalent classical baseline. In addition, we include resource estimates for evaluating the model on quantum hardware, and provide an open-source implementation for classical simulation. We conclude by highlighting the generality of Quixer, showing that its parameterised components can be substituted with fixed structures to yield new classes of quantum transformers.
- [36] arXiv:2406.04307 [pdf, ps, html, other]
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Title: High-precision and low-depth eigenstate property estimation: theory and resource estimationComments: 48 pages, 7 figures, and 4 tablesSubjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Computational Physics (physics.comp-ph)
Estimating the eigenstate properties of quantum many-body systems is a long-standing, challenging problem for both classical and quantum computing. For the task of eigenstate preparation, quantum signal processing (QSP) has established near-optimal query complexity $O( \Delta^{-1} \log(\epsilon^{-1}) )$ by querying the block encoding of the Hamiltonian $H$ where $\Delta$ is the energy gap and $\epsilon$ is the target precision. However, QSP is challenging for both near-term noisy quantum computers and early fault-tolerant quantum computers (FTQC), which are limited by the number of logical qubits and circuit depth. To date, early FTQC algorithms have focused on querying the perfect time evolution $e^{-iHt}$. It remains uncertain whether early FTQC algorithms can maintain good asymptotic scaling at the gate level. Moreover, when considering qubit connectivity, the circuit depth of existing FTQC algorithms may scale suboptimally with system size. Here, we present a full-stack design of a random sampling algorithm for estimating the eigenenergy and the observable expectations on the eigenstates, which can achieve high precision and good system size scaling. The gate complexity has a logarithmic dependence on precision $ {O}(\log^{1+o(1)} (1/\epsilon))$ for generic Hamiltonians, which cannot achieved by methods using Trottersiation to realise $e^{-iHt}$ like in QETU. For $n$-qubit lattice Hamiltonians, our method achieves near-optimal system size dependence with the gate complexity $O(n^{1+o(1)})$. When restricting the qubit connectivity to a linear nearest-neighbour architecture, The method shows advantages in circuit depth, with $O(n^{o(1)})$ for lattice models and $O(n^{2+o(1)})$ for electronic structure problems. We compare the resource requirements (CNOT gates, T gates and qubit numbers) by phase estimation, QSP, and QETU, in lattice and molecular problems.
New submissions for Friday, 7 June 2024 (showing 36 of 36 entries )
- [37] arXiv:2406.03449 (cross-list from cond-mat.str-el) [pdf, ps, html, other]
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Title: Global fermionic mode optimization via swap gatesComments: 5 pages, 4 figuresSubjects: Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
We propose a general approach to find an optimal representation of a quantum many body wave function for a given error margin via global fermionic mode optimization. The stationary point on a fixed rank matrix product state manifold is obtained via a joint optimization on the Grassman manifold [Phys. Rev. Lett. 117, 210402] together with swap gates controlled permutations. The minimization of the global quantity, the block entropy area, guarantees that the method fulfills all criteria with respect to partial derivatives. Numerical results via large scale density matrix renormalization group simulations on strongly correlated molecular systems and two-dimensional fermionic lattice models are discussed.
- [38] arXiv:2406.03502 (cross-list from math.OC) [pdf, ps, html, other]
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Title: Quantum-Inspired Mean Field Probabilistic Model for Combinatorial Optimization ProblemsComments: 13 pages, 10 figuresSubjects: Optimization and Control (math.OC); Quantum Physics (quant-ph)
Combinatorial optimization problems are pivotal across many fields. Among these, Quadratic Unconstrained Binary Optimization (QUBO) problems, central to fields like portfolio optimization, network design, and computational biology, are NP-hard and require exponential computational resources. To address these challenges, we develop a novel Quantum-Inspired Mean Field (QIMF) probabilistic model that approximates solutions to QUBO problems with enhanced accuracy and efficiency. The QIMF model draws inspiration from quantum measurement principles and leverages the mean field probabilistic model. We incorporate a measurement grouping technique and an amplitude-based shot allocation strategy, both critical for optimizing cost functions with a polynomial speedup over traditional methods. Our extensive empirical studies demonstrate significant improvements in solution evaluation for large-scale problems of portfolio selection, the weighted maxcut problem, and the Ising model. Specifically, using S&P 500 data from 2022 and 2023, QIMF improves cost values by 152.8% and 12.5%, respectively, compared to the state-of-the-art baselines. Furthermore, when evaluated on increasingly larger datasets for QUBO problems, QIMF's scalability demonstrates its potential for large-scale QUBO challenges.
- [39] arXiv:2406.03521 (cross-list from cond-mat.stat-mech) [pdf, ps, html, other]
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Title: Mpemba effects in open nonequilibrium quantum systemsComments: 11 pages, 11 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
We generalize the classical thermal Mpemba effect (where an initially hot system relaxes faster to the final equilibrium state than a cold one) to open quantum systems coupled to several reservoirs. We show that, in general, two different types of quantum Mpemba effects are possible. They may be distinguished by quantum state tomography. However, the existence of a quantum Mpemba effect (without determining the type) can already be established by measuring simpler observables such as currents or energies. We illustrate our general results for the experimentally feasible case of an interacting two-site Kitaev model coupled to two metallic leads.
- [40] arXiv:2406.03524 (cross-list from hep-th) [pdf, ps, html, other]
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Title: Spread complexity and localization in $\mathcal{PT}$-symmetric systemsComments: 6 pages, 4 figures main text plus appendix 3 pages, 3 figuresSubjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
We present a framework for investigating wave function spreading in $\mathcal{PT}$-symmetric quantum systems using spread complexity and spread entropy. We consider a tight-binding chain with complex on-site potentials at the boundary sites. In the $\mathcal{PT}$-unbroken phase, the wave function is delocalized. We find that in the $\mathcal{PT}$-broken phase, it becomes localized on one edge of the tight-binding lattice. This localization is a realization of the non-Hermitian skin effect. Localization in the $\mathcal{PT}$-broken phase is observed both in the lattice chain basis and the Krylov basis. Spread entropy, entropic complexity, and a further measure that we term the Krylov inverse participation ratio probe the dynamics of wave function spreading and quantify the strength of localization probed in the Krylov basis. The number of Krylov basis vectors required to store the information of the state reduces with the strength of localization. Our results demonstrate how measures in Krylov space can be used to characterize the non-hermitian skin effect and its localization phase transition.
- [41] arXiv:2406.03536 (cross-list from hep-ph) [pdf, ps, html, other]
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Title: Towards Quantum Computing Timelike Hadronic Vacuum Polarization and Light-by-Light Scattering: Schwinger Model TestsComments: 7 pages, 5 figuresSubjects: High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)
Hadronic vacuum polarization (HVP) and light-by-light scattering (HLBL) are crucial for evaluating the Standard Model predictions concerning the muon's anomalous magnetic moment. However, direct first-principle lattice gauge theory-based calculations of these observables in the timelike region remain challenging. Discrepancies persist between lattice quantum chromodynamics (QCD) calculations in the spacelike region and dispersive approaches relying on experimental data parametrization from the timelike region. Here, we introduce a methodology employing 1+1-dimensional quantum electrodynamics (QED), i.e. the Schwinger Model, to investigate the HVP and HLBL. To that end, we use both tensor network techniques, specifically matrix product states, and classical emulators of digital quantum computers. Demonstrating feasibility in a simplified model, our approach sets the stage for future endeavors leveraging digital quantum computers.
- [42] arXiv:2406.03609 (cross-list from physics.optics) [pdf, ps, other]
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Title: Modulated Ringdown Comb Interferometry for next-generation high complexity trace gas sensingSubjects: Optics (physics.optics); Chemical Physics (physics.chem-ph); Quantum Physics (quant-ph)
Gas samples relevant to health and environment typically contain a plethora of molecular species that span a huge concentration dynamic range. High-concentration molecules impose a strong absorption background that hinders robust identification of low-concentration species. While mid-infrared frequency comb spectroscopy with high-finesse cavity enhancement has realized many of the most sensitive multi-species trace gas detection to date, its robust performance requires gas samples to contain only weak absorption features to avoid dispersing cavity resonances from the comb line frequencies. Here we introduce a new technique that is free from this restriction, thus enabling the development of next-generation multi-species trace gas sensing with broad applicability to complex and dynamic molecular compositions. The principle of Modulated Ringdown Comb Interferometry is to resolve ringdown dynamics carried by massively parallel comb lines transmitted through a length-modulated cavity. This method leverages both periodicity of the field dynamics and Doppler frequency shifts introduced from a Michelson interferometer. Scalable enhancement of both spectral coverage and cavity finesse is enabled with dispersion immune and high-efficiency data collection. Built upon this platform, we realize in the mid-infrared a product of finesse and spectral coverage that is orders of magnitude better than all prior experiments. We demonstrate the power of this technique by measuring highly dispersive exhaled human breath samples over a vastly expanded spectral coverage of 1,010 cm-1 and with cavity finesse of 23,000. This allows for the first time simultaneous quantification of 20 distinct molecular species at > 1 part-per-trillion sensitivity with their concentrations varying by 7 orders of magnitude.
- [43] arXiv:2406.03624 (cross-list from cond-mat.mes-hall) [pdf, ps, html, other]
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Title: Entanglement harvesting in buckled honeycomb lattices by vacuum fluctuations in a microcavityComments: 10 pages, 6 figuresSubjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)
We study the entanglement harvesting between two identical buckled honeycomb lattices placed inside a planar microcavity. By applying time dependent perturbation theory, we obtain quantum correlations between both layers induced by the cavity field. Considering the vacuum state as the initial state of the cavity field and tracing out the time-evolved degrees of freedom, we analyze the entanglement formation using the concurrence measure. We show that the concurrence depends on the virtual photon exchanged and the positions of the layer through the interlayer photon propagator. Furthermore, we find that the formation of entanglement between equal energy electrons tends to be enhanced when they move in perpendicular directions. Our results indicate that a buckled honeycomb structure and a large spin-orbit interaction favor the entanglement harvesting.
- [44] arXiv:2406.03690 (cross-list from math.OC) [pdf, ps, html, other]
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Title: AMPIC: Adaptive Model Predictive Ising Controller for large-scale urban traffic signalsComments: 17 pages, 8 figuresSubjects: Optimization and Control (math.OC); Emerging Technologies (cs.ET); Systems and Control (eess.SY); Quantum Physics (quant-ph)
Realizing smooth traffic flow is important for achieving carbon neutrality. Adaptive traffic signal control, which considers traffic conditions, has thus attracted attention. However, it is difficult to ensure optimal vehicle flow throughout a large city using existing control methods because of their heavy computational load. Here, we propose a control method called AMPIC (Adaptive Model Predictive Ising Controller) that guarantees both scalability and optimality. The proposed method employs model predictive control to solve an optimal control problem at each control interval with explicit consideration of a predictive model of vehicle flow. This optimal control problem is transformed into a combinatorial optimization problem with binary variables that is equivalent to the so-called Ising problem. This transformation allows us to use an Ising solver, which has been widely studied and is expected to have fast and efficient optimization performance. We performed numerical experiments using a microscopic traffic simulator for a realistic city road network. The results show that AMPIC enables faster vehicle cruising speed with less waiting time than that achieved by classical control methods, resulting in lower CO2 emissions. The model predictive approach with a long prediction horizon thus effectively improves control performance. Systematic parametric studies on model cities indicate that the proposed method realizes smoother traffic flows for large city road networks. Among Ising solvers, D-Wave's quantum annealing is shown to find near-optimal solutions at a reasonable computational cost.
- [45] arXiv:2406.03705 (cross-list from cond-mat.mes-hall) [pdf, ps, html, other]
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Title: Coherent control of a triangular exchange-only spin qubitEdwin Acuna, Joseph D. Broz, Kaushal Shyamsundar, Antonio B. Mei, Colin P. Feeney, Valerie Smetanka, Tiffany Davis, Kangmu Lee, Maxwell D. Choi, Brydon Boyd, June Suh, Wonill D. Ha, Cameron Jennings, Andrew S. Pan, Daniel S. Sanchez, Matthew D. Reed, Jason R. PettaSubjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)
We demonstrate coherent control of a three-electron exchange-only spin qubit with the quantum dots arranged in a close-packed triangular geometry. The device is tuned to confine one electron in each quantum dot, as evidenced by pairwise charge stability diagrams. Time-domain control of the exchange coupling is demonstrated and qubit performance is characterized using blind randomized benchmarking, with an average single-qubit gate fidelity F = 99.84%. The compact triangular device geometry can be readily scaled to larger two-dimensional quantum dot arrays with high connectivity.
- [46] arXiv:2406.03863 (cross-list from physics.optics) [pdf, ps, other]
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Title: Topological Materials for Near-Field Radiative Heat TransferAzadeh Didari-Bader, Seonyeong Kim, Heejin Choi, Sunae Seo, Piyali Biswas, Heejeong Jeong, Chang-Won LeeSubjects: Optics (physics.optics); Quantum Physics (quant-ph)
Topological materials provide a platform that utilizes the geometric characteristics of structured materials to control the flow of waves, enabling unidirectional and protected transmission that is immune to defects or impurities. The topologically designed photonic materials can carry quantum states and electromagnetic energy, benefiting nanolasers or quantum photonic systems. This article reviews recent advances in the topological applications of photonic materials for radiative heat transfer, especially in the near field. When the separation distance between media is considerably smaller than the thermal wavelength, the heat transfer exhibits super-Planckian behavior that surpasses Planck's blackbody predictions. Near-field thermal radiation in subwavelength systems supporting surface modes has various applications, including nanoscale thermal management and energy conversion. Photonic materials and structures that support topological surface states show immense potential for enhancing or suppressing near-field thermal radiation. We present various topological effects, such as periodic and quasi-periodic nanoparticle arrays, Dirac and Weyl semimetal-based materials, structures with broken global symmetries, and other topological insulators, on near-field heat transfer. Also, the possibility of realizing near-field thermal radiation in such topological materials for alternative thermal management and heat flux guiding in nano-scale systems is discussed based on the existing technology.
- [47] arXiv:2406.03911 (cross-list from physics.atom-ph) [pdf, ps, html, other]
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Title: Analyzing the sensitivity of an atom interferometer with a phase modulation readout schemeComments: 9 pages, 4 figuresSubjects: Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
The sensitivity of an interferometer depends on its readout scheme. However, little attention has been paid to the readout schemes of atom interferometers from the viewpoint of their sensitivity. The difference in sensitivity between readout schemes or their optimization has not been considered in the literature. Herein, we analytically calculate the sensitivities of an atom interferometer with typical readout schemes by applying the two-photon formalism, which was developed for optical interferometers to deal with quantum noise. Our calculations reveal that by using sinusoidal phase modulation, the sensitivity can surpass that obtained by the conventional phase sweeping scheme. The superiority of this phase modulation scheme for both cold and thermal atomic beams is demonstrated. In addition, we show that the phase modulation scheme is advantageous for atom-flux fluctuation and resists atom-flux drift. This study performs a general analysis of the sensitivity of atom interferometers and identifies an advantageous readout scheme.
- [48] arXiv:2406.03927 (cross-list from cond-mat.mes-hall) [pdf, ps, other]
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Title: Engineering open-shell extended edge states in chiral graphene nanoribbons on MgOAmelia Domínguez-Celorrio, Leonard Edens, Sofía Sanz, Manuel Vilas-Varela, Jose Martinez-Castro, Diego Peña, Véronique Langlais, Thomas Frederiksen, José I. Pascual, David SerrateSubjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)
Graphene nanostructures are a promising platform for engineering electronic states with tailored magnetic and quantum properties. Synthesis strategies on metallic substrates have made it possible to manufacture atomically precise nanographenes with controlled size, shape and edge geometry. In these nanographenes, finite spin magnetic moment can arise as a result of many-body interactions in molecular orbitals with $\pi$-conjugated character and subject to strong spatial confinement, for example at the zig-zag edges. However, owing to the mixing of the molecular orbitals and metallic states from the catalysing substrate, most of their expected quantum phenomenology is severely hindered. The use of in-situ ultra-thin decoupling layers can impede nanographene-metal hybridization and facilitate the expression of predicted properties. Here we show that the edges of narrow chiral graphene nanoribbons (GNRs) over MgO monolayers on Ag(001) can host integer charge and spin-1/2 frontier states. The electron occupation varies with the GNR length, which alternates even or odd number of electrons, thus resulting correspondingly in a non-magnetic closed-shell state or an open-shell paramagnetic system. For the latter, we found the spectral fingerprint of a narrow Coulomb correlation gap. Charged states, up to 19 additional electrons, were identified by comparing mean-field Hubbard (MFH) simulations of the density of states with experimental maps of the discretized molecular orbitals acquired with a scanning tunnelling microscope (STM). In consideration of the length-dependent magnetic moment and the discrete nature of the electronic structure, we envisage that GNRs supported by thin insulating films can be used as tailor-made active elements in quantum sensing and quantum information processing.
- [49] arXiv:2406.03983 (cross-list from cond-mat.stat-mech) [pdf, ps, html, other]
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Title: Level statistics detect generalized symmetriesComments: 5 pages main, 3 pages supplementalSubjects: Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
Level statistics are a useful probe for detecting symmetries and distinguishing integrable and non-integrable systems. I show by way of several examples that level statistics detect the presence of generalized symmetries that go beyond conventional lattice symmetries and internal symmetries. I consider non-invertible symmetries through the example of Kramers-Wannier duality at an Ising critical point, symmetries with nonlocal generators through the example of a spin-$1$ anisotropic Heisenberg chain, and $q$-deformed symmetries through an example closely related to recent work on $q$-deformed SPT phases. In each case, conventional level statistics detect the generalized symmetries, and these symmetries must be resolved before seeing characteristic level repulsion in non-integrable systems. For the $q$-deformed symmetry, I discovered via level statistics a $q$-deformed generalization of inversion that is interesting in its own right and that may protect $q$-deformed SPT phases.
- [50] arXiv:2406.04015 (cross-list from physics.atom-ph) [pdf, ps, html, other]
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Title: Identification of highly-forbidden optical transitions in highly charged ionsShuying Chen, Lukas J. Spieß, Alexander Wilzewski, Malte Wehrheim, Kai Dietze, Ivan Vybornyi, Klemens Hammerer, Jose R. Crespo Lopez-Urrutia, Piet O. SchmidtSubjects: Atomic Physics (physics.atom-ph); Instrumentation and Detectors (physics.ins-det); Optics (physics.optics); Plasma Physics (physics.plasm-ph); Quantum Physics (quant-ph)
Optical clocks represent the most precise experimental devices, finding application in fields spanning from frequency metrology to fundamental physics. Recently, the first highly charged ions (HCI) based optical clock was demonstrated using Ar$^{13+}$, opening up a plethora of novel systems with advantageous atomic properties for high accuracy clocks. While numerous candidate systems have been explored theoretically, the considerable uncertainty of the clock transition frequency for most species poses experimental challenges. Here, we close this gap by exploring quantum logic-inspired experimental search techniques for sub-Hertz clock transitions in HCI confined to a linear Paul trap. These techniques encompass Rabi excitation, an optical dipole force (ODF) approach, and linear continuous sweeping (LCS) and their applicability for different types of HCI. Through our investigation, we provide tools to pave the way for the development of exceptionally precise HCI-based optical clocks.
- [51] arXiv:2406.04061 (cross-list from cs.CR) [pdf, ps, html, other]
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Title: Computing $\varphi(N)$ for an RSA module with a single quantum querySubjects: Cryptography and Security (cs.CR); Quantum Physics (quant-ph)
In this paper we give a polynomial time algorithm to compute $\varphi(N)$ for an RSA module $N$ using as input the order modulo $N$ of a randomly chosen integer. The algorithm consists only on a computation of a greatest common divisor, two multiplications and a division. The algorithm works with a probability of at least $1-\frac{C\log\log N}{N^{1/2}}$.
- [52] arXiv:2406.04125 (cross-list from hep-th) [pdf, ps, html, other]
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Title: Particle creation using the classical stochastic methodComments: 8 pagesSubjects: High Energy Physics - Theory (hep-th); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)
We compute the particle creation of a harmonic oscillator using the classical stochastic method. This method reproduces all the vacuum expectation values in quantum theory. We prepare the vacuum state at the initial time and evolve it over time using Langevin equations of motion. By averaging over the ensemble, we compute the energy of the state at the final time and determine the amount of particles created. We verify that the particle creation agrees with predictions from quantum theory.
- [53] arXiv:2406.04183 (cross-list from cond-mat.dis-nn) [pdf, ps, html, other]
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Title: Manipulating the Relaxation Time of Boundary-Dissipative Systems through Bond DissipationSubjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)
Relaxation time plays a crucial role in describing the relaxation processes of quantum systems. We study the effect of a type of bond dissipation on the relaxation time of boundary dissipative systems and find that it can change the scaling of the relaxation time $T_c\sim L^{z}$ from $z=3$ to a value significantly less than $3$. We further reveal that the reason such bond dissipation can significantly reduce the relaxation time is that it can selectively target specific states. For Anderson localized systems, the scaling behavior of the relaxation time changes from an exponential form to a power-law form as the system size varies. This is because the bond dissipation we consider can not only select specific states but also disrupt the localization properties. Our work reveals that in open systems, one type of dissipation can be used to regulate the effects produced by another type of dissipation.
- [54] arXiv:2406.04296 (cross-list from cond-mat.stat-mech) [pdf, ps, other]
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Title: Translation symmetry restoration under random unitary dynamicsComments: 6+4 pages, 3 figuresSubjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
The finite parts of a large, locally interacting many-body system prepared out-of-equilibrium eventually equilibrate. Characterising the underlying mechanisms of this process and its timescales, however, is particularly hard as it requires to decouple universal features from observable-specific ones. Recently, new insight came by studying how certain symmetries of the dynamics that are broken by the initial state are restored at the level of the reduced state of a given subsystem. This provides a high level, observable-independent probe. Until now this idea has been applied to the restoration of internal symmetries, e.g. U(1) symmetries related to charge conservation. Here we show that that the same logic can be applied to the restoration of space-time symmetries, and hence can be used to characterise the relaxation of fully generic systems. We illustrate this idea by considering the paradigmatic example of "generic" many-body dynamics, i.e. a local random unitary circuit. We show that, surprisingly, the restoration of translation symmetry in these systems only happens on time-scales proportional to the subsystem's volume. In fact, for large enough subsystems the time of symmetry restoration becomes initial-state independent (as long as the latter breaks the symmetry at time zero) and coincides with the thermalisation time. For intermediate subsystems, however, one can observe the so-called "quantum Mpemba effect", where the state of the system restores a symmetry faster if it is initially more asymmetric.
- [55] arXiv:2406.04310 (cross-list from hep-th) [pdf, ps, html, other]
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Title: Neural Networks Assisted Metropolis-Hastings for Bayesian Estimation of Critical Exponent on Elliptic Black Hole Solution in 4D Using Quantum Perturbation TheoryComments: 33 pages, 10 figuresSubjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
The critical gravitational collapse is known to produce continuous self-similar solutions characterized by the Choptuik critical exponent, $\gamma$. We examine all solutions within the complete domains of the linear perturbation equations, considering the numerical measurement errors. Specifically, we study quantum perturbation theory for the four-dimensional Einstein-axion-dilaton system of the elliptic class of $\text{SL}(2,\mathbb{R})$ transformations. We developed a novel artificial neural network-assisted Metropolis-Hastings based on quantum perturbation theory to find the critical exponent in a Bayesian framework. Unlike existing methods, this new probabilistic approach identifies the available deterministic solutions and explores the range of physically distinguishable critical exponents that may arise due to numerical measurement errors.
Cross submissions for Friday, 7 June 2024 (showing 19 of 19 entries )
- [56] arXiv:2108.01183 (replaced) [pdf, ps, html, other]
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Title: Long-Time Error-Mitigating Simulation of Open Quantum Systems on Near Term Quantum ComputersSubjects: Quantum Physics (quant-ph)
We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates. We simulate two systems of electrons coupled to an infinite thermal bath: 1) a system of dissipative free electrons in a driving electric field; and 2) the thermalization of two interacting electrons in a single orbital in a magnetic field -- the Hubbard atom. These problems are solved using IBM quantum computers, showing no signs of decreasing fidelity at long times. Our results demonstrate that algorithms for simulating open quantum systems are able to far outperform similarly complex non-dissipative algorithms on noisy hardware. Our two examples show promise that the driven-dissipative quantum many-body problem can eventually be solved on quantum computers.
- [57] arXiv:2111.05383 (replaced) [pdf, ps, html, other]
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Title: Path Integrals from Spacetime Quantum ActionsComments: 20 pages, 3 figures, improved presentationSubjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
The possibility of extending the canonical formulation of quantum mechanics (QM) to a space-time symmetric form has recently attracted wide interest. In this context, a recent proposal has shown that a spacetime symmetric many-body extension of the Page and Wootters mechanism naturally leads to the so-called Quantum Action (QA) operator, a quantum version of the action of classical mechanics. In this work, we focus on connecting the QA with the well-established Feynman's Path Integral (PI). In particular, we present a novel formalism which allows one to identify the "sum over histories" with a quantum trace, where the role of the classical action is replaced by the corresponding QA. The trace is defined in the extended Hilbert space resulting from assigning a conventional Hilbert space to each time slice and then taking their tensor product. The formalism opens the way to the application of quantum computation protocols to the evaluation of PIs and general correlation functions, and reveals that different representations of the PI arise from distinct choices of basis in the evaluation of the same trace expression. The Hilbert space embedding of the PIs also discloses a new approach to their continuum time limit. Finally, we discuss how the ensuing canonical-like version of QM inherits many properties from the PI formulation, thus allowing an explicitly covariant treatment of spacetime symmetries.
- [58] arXiv:2302.02918 (replaced) [pdf, ps, html, other]
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Title: Optimisation of time-ordered processes in the finite and asymptotic regimeComments: Close to published versionJournal-ref: PRX Quantum 5, 020351 (2024)Subjects: Quantum Physics (quant-ph); Optimization and Control (math.OC)
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement detection protocol; (c) let the computer invent an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios.
- [59] arXiv:2303.06559 (replaced) [pdf, ps, html, other]
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Title: Delay-induced spontaneous dark state generation from two distant excited atomsSubjects: Quantum Physics (quant-ph)
We investigate the collective non-Markovian dynamics of two fully excited two-level atoms coupled to a one-dimensional waveguide in the presence of delay. We demonstrate that analogous to the well-known superfluorescence phenomena, where an inverted atomic ensemble synchronizes to enhance its emission, there is a `subfluorescence' effect that synchronizes the atoms into an entangled dark state depending on the interatomic separation. Our results are pertinent to long-distance quantum networks, presenting a mechanism for spontaneous entanglement generation between distant quantum emitters.
- [60] arXiv:2303.18095 (replaced) [pdf, ps, other]
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Title: Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculationsComments: 32 pages, 24 figures, 3 tablesSubjects: Quantum Physics (quant-ph)
Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is employed to obtain the ground state with higher accuracy than QMC alone. We propose an algorithm combining QC-QMC with a hybrid tensor network to extend the applicability of QC-QMC beyond a single quantum device size. In a two-layer quantum-quantum tree tensor, our algorithm for the larger trial wave function can be executed than preparable wave function in a device. Our algorithm is evaluated on the Heisenberg chain model, graphite-based Hubbard model, hydrogen plane model, and MonoArylBiImidazole using full configuration interaction QMC. Our algorithm can achieve energy accuracy (specifically, variance) several orders of magnitude higher than QMC, and the hybrid tensor version of QMC gives the same energy accuracy as QC-QMC when the system is appropriately decomposed. Moreover, we develop a pseudo-Hadamard test technique that enables efficient overlap calculations between a trial wave function and an orthonormal basis state. In a real device experiment by using the technique, we obtained almost the same accuracy as the statevector simulator, indicating the noise robustness of our algorithm. These results suggests that the present approach will pave the way to electronic structure calculation for large systems with high accuracy on current quantum devices.
- [61] arXiv:2305.16939 (replaced) [pdf, ps, other]
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Title: Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary statesComments: The paper was changed to different one due to addition of new material and an author. A title and authors of the paper were changed. Accordingly we withdraw an old paper and submit new paperSubjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Atomic Physics (physics.atom-ph)
Orthogonality of eigenstates of different energies and its implications in potential scattering are unlabeled. Scalar products of scattering states of different energies are found to have finite non-orthogonal terms in potentials of finite widths. Their superpositions have time-dependent norms, and are not suitable for isolate states. In these systems, a perturbative method and a variational method are viable methods for finding a rigorous transition probability that describes phenomena completely. In various exceptional potentials, an orthogonality is satisfied.
- [62] arXiv:2307.15226 (replaced) [pdf, ps, other]
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Title: Factory-based Fault-tolerant Preparation of Quantum Polar Codes Encoding One logical QubitComments: 24 pages, 11 figuresSubjects: Quantum Physics (quant-ph)
A fault-tolerant way to prepare logical code-states of Q1 codes, i.e., quantum polar codes encoding one qubit, has been recently proposed. The fault tolerance therein is guaranteed by an error detection gadget, where if an error is detected during the preparation, one discards entirely the preparation. Due to error detection, the preparation is probabilistic, and its success rate, referred to as the preparation rate, decreases rapidly with the code-length, preventing the preparation of code-states of large code-lengths. In this paper, to improve the preparation rate, we consider a factory preparation of Q1 code-states, where one attempts to prepare several copies of Q1 code-states in parallel. Using an extra scheduling step, we can avoid discarding the preparation entirely, every time an error is detected, hence, achieving an increased preparation rate in turn. We further provide a theoretical method to estimate preparation and logical error rates of Q1 codes, prepared using factory preparation, which is shown to tightly fit the Monte-Carlo simulation based numerical results. Therefore, our theoretical method is useful for providing estimates for large code-lengths, where Monte-Carlo simulations are practically not feasible. Our numerical results, for a circuit-level depolarizing noise model, indicate that the preparation rate increases significantly, especially for large code-length N. For example, for N = 256, it increases from 0.02\% to 27\% for a practically interesting physical error rate of p = 10^{-3}. Remarkably, a Q1 code with N = 256 achieves logical error rates around 10^{-11} and 10^{-15} for p = 10^{-3} and p = 3 x 10^{-4}, respectively. This corresponds to an improvement of about three orders of magnitude compared to a surface code with similar code-length and minimum distance, thus showing the promise of the proposed scheme for large-scale fault-tolerant quantum computing.
- [63] arXiv:2308.13045 (replaced) [pdf, ps, other]
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Title: Single Photon Quantum Ranging: When Sequential Decoding Meets High Dimensional EntanglementComments: Needs major revisionsSubjects: Quantum Physics (quant-ph)
We consider the quantum ranging problem in the low noise level per mode and low reflectivity (high loss) regime. We focus on single photon transmission strategies and propose a novel approach that combines high dimensional time-bin entanglement at the transmitter with a carefully constructed sequential decision rule at the detector. Our analytical results establish the significant performance gains that can be leveraged from this approach in a range of operating parameters, as compared to the single photon classical approach, the two-mode squeezed vacuum ranging scheme proposed earlier, and even the block-based classical scheme. One can attribute this performance gain to 1) the ability of the high dimensional time-bin entangled signaling to offer a very fine range resolution with a single transmitted photon and 2) the ability of the sequential decision rule to minimize the average number of transmitted photon subject to a constraint on the probability of error. While our analysis is limited to the low energy/low noise regime, we conjecture that the proposed approach's superior performance extends to a wider range of scenarios which should motivate further analytical and experimental investigations.
- [64] arXiv:2309.05290 (replaced) [pdf, ps, html, other]
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Title: Solving Systems of Linear Equations: HHL from a Tensor Networks PerspectiveAlejandro Mata Ali, Iñigo Perez Delgado, Marina Ristol Roura, Aitor Moreno Fdez. de Leceta, Sebastián V. RomeroComments: 7 pages, 7 figuresSubjects: Quantum Physics (quant-ph); Computational Physics (physics.comp-ph)
We present an algorithm for solving systems of linear equations based on the HHL algorithm with a novel qudits methodology, a generalization of the qubits with more states, to reduce the number of gates to be applied and the amount of resources. Based on this idea, we perform a quantum-inspired version on tensor networks, taking advantage of their ability to perform non-unitary operations such as projection. The main novelty of this proposal is to perform a simulation as efficient as possible of the HHL algorithm in order to benchmark the algorithm steps according to its input parameters and the input matrix. Finally, we use this algorithm to obtain a solution for the harmonic oscillator with an external force, the forced damped oscillator and the 2D static heat equation differential equations.
- [65] arXiv:2312.05697 (replaced) [pdf, ps, html, other]
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Title: Environment induced dynamical quantum phase transitions in two-qubit Rabi modelComments: 8 pages, 6 figures in main text; 8 pages, 6 figures in supplemental materialSubjects: Quantum Physics (quant-ph)
The physics of quantum states beyond thermodynamic equilibrium represents a fascinating and cutting-edge research. Using numerical state-of-the-art approaches, we observe dynamical quantum phase transitions in the dissipative two-qubit Rabi model. By quenching the qubits-oscillator coupling, the system (Rabi + Environment) exhibits dynamical quantum phase transitions signalled by kinks of Loschmidt echo's rate function at parameter values close to thermodynamic transition. Notably, these transitions also manifest in two-qubit entanglement. While at equilibrium one class of Beretzinski-Kosterlitz-Thouless-type transitions occurs, non-equilibrium conditions reveal two classes of dynamical critical phenomena, depending on qubits' interactions and entanglement. When qubits directly interact, the kink critical exponent describes a linear behavior, reminiscent of nearest neighbors Ising chains, with short-range interactions dominating at short times. Conversely, non-interacting qubits exhibit critical exponents much smaller than unity due to bath-induced long-range interactions. These findings shed light on the complex behavior of dynamical quantum phase transitions in non-integrable models, showing unusual entanglement features and the environment's significant role.
- [66] arXiv:2312.09679 (replaced) [pdf, ps, html, other]
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Title: Optimal joint cutting of two-qubit rotation gatesChristian Ufrecht, Laura S. Herzog, Daniel D. Scherer, Maniraman Periyasamy, Sebastian Rietsch, Axel Plinge, Christopher MutschlerJournal-ref: Phys. Rev. A 109, 052440 (2024)Subjects: Quantum Physics (quant-ph); Computational Physics (physics.comp-ph)
Circuit cutting, the partitioning of quantum circuits into smaller independent fragments, has become a promising avenue for scaling up current quantum-computing experiments. Here, we introduce a scheme for joint cutting of two-qubit rotation gates based on a virtual gate-teleportation protocol. By that, we significantly lower the previous upper bounds on the sampling overhead and prove optimality of the scheme. Furthermore, we show that no classical communication between the circuit partitions is required. For parallel two-qubit rotation gates we derive an optimal ancilla-free decomposition, which include CNOT gates as a special case.
- [67] arXiv:2312.11685 (replaced) [pdf, ps, html, other]
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Title: Interplay between the Hilbert-space dimension of the control system and the memory induced by quantum SWITCHComments: New results added ; 17 pages, 4 figuresSubjects: Quantum Physics (quant-ph)
Several recent studies have demonstrated the utility of the quantum SWITCH as an important resource for enhancing the performance of various information processing tasks. In a quantum SWITCH, the advantages appear significantly due to the coherent superposition of alternative configurations of the quantum components which are controlled by an additional control system. Here we explore the impact of increasing the Hilbert-space dimension of the control system on the performance of the quantum SWITCH. In particular, we focus on a quantifier of the quantum SWITCH through the emergence of non-Markovianity and explicitly study their behavior when we increase the Hilbert-space dimension of the control system. We observe that increasing the Hilbert-space dimension of the control system leads to the corresponding enhancement of the non-Markovian memory induced by it. Our study demonstrates how the dimension of the control system can be harnessed to improve the quantum SWITCH-based information processing or communication tasks
- [68] arXiv:2401.01562 (replaced) [pdf, ps, html, other]
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Title: Evidence-based certification of quantum dimensionsY. S. Teo, H. Jeong, N. Prasannan, B. Brecht, C. Silberhorn, M. Evans, D. Mogilevtsev, L. L. Sanchez-SotoComments: 11 pages, 4 figures, companion article in arXiv:2406.03343Subjects: Quantum Physics (quant-ph)
Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and continuous variables that is fully evidence-based, relying solely on the experimental data collected and no other unjustified assumptions whatsoever. Using the Bayesian concept of relative belief, we take the effective dimension of the state as the smallest one such that the posterior probability is larger than the prior, as dictated by the data. The posterior probabilities associated with the relative-belief ratios measure the strength of the evidence provide by these ratios so that we can assess whether there is weak or strong evidence in favor or against a particular dimension. Using experimental data from spectral-temporal and polarimetry measurements, we demonstrate how to correctly assign Bayesian plausible error bars for the obtained effective dimensions. This makes relative belief a conservative and easy-to-use model-selection method for any experiment.
- [69] arXiv:2401.08110 (replaced) [pdf, ps, html, other]
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Title: Success probabilities in time-reversal based hybrid quantum state transferComments: manuscript: 17 pages, 7 figures; references: 9 pages; supplemental material: 39 pages, 9 figuresSubjects: Quantum Physics (quant-ph)
We consider two memory nodes of a quantum network connected by flying qubits. We are particularly interested in the case where a flying qubit produced by one node has to be transformed before it can interface efficiently with the next node. Such transformations can be utilized as a key part of the distribution of quantum states and hence entanglement between the nodes of a hybrid quantum network linking together different quantum technologies. We show how and why the probability of interfacing successfully is determined by the overlap of the spectral shape of the actual flying qubit and the ideal shape. This allows us to analytically and numerically analyze how the probability of success is impacted by realistic errors, and show the utility of our scheme (in consonance with known error correction methods) in connecting hybrid nodes of a quantum network. We focus here on a concrete implementation in which the memory nodes consist of three-level atoms in cavities and the flying qubits are photons.
- [70] arXiv:2401.17537 (replaced) [pdf, ps, other]
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Title: Complementary Relationships between Entanglement and MeasurementSubjects: Quantum Physics (quant-ph)
Complementary relationships exist regarding interference properties of particles such as pattern visibility, predictability and distinguishability. Additionally, relationships are known between information gain $G$ and measurement disturbance $F$ for entangled spin pairs. The question of whether a similar complementary relationship between entanglement and measurement occurs is examined herein. For qubit systems, both measurement on a single system and measurements on a bipartite system are considered in regards to the entanglement. It is proven that $\overline{E}+D\le 1$ holds where $\overline{E}$ is the average entanglement after a measurement is made and for which $D$ is a measure of the measurement disturbance of a single measurement. For measurements on a bipartite system shared by Alice and Bob ,it is shown that $\overline{E}+G\le 1$ where $G$ is the maximum information gain regarding Alice's result that can be obtained by Bob. These results are generalized for arbitrary initial mixed states and as well to non-Hermitian operators. In the case of maximally entangled initial states, it is found that $D\le E_{L}$ and $G\le E_{L}$ where $E_{L}$ is the entanglement loss due to measurement by Alice. We conclude that the amount of disturbance and information gain that one can gain are strictly limited by entanglement.
- [71] arXiv:2403.02057 (replaced) [pdf, ps, html, other]
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Title: Revisiting fixed-point quantum search: proof of the quasi-Chebyshev lemmaSubjects: Quantum Physics (quant-ph)
The original Grover's algorithm suffers from the souffle problem, which means that the success probability of quantum search decreases dramatically if the iteration time is too small or too large from the right time. To overcome the souffle problem, the fixed-point quantum search with an optimal number of queries was proposed [Phys. Rev. Lett. 113, 210501 (2014)], which always finds a marked state with a high probability when a lower bound of the proportion of marked states is given. The fixed-point quantum search relies on a key lemma regarding the explicit formula of recursive quasi-Chebyshev polynomials, but its proof is not given explicitly. In this work, we give a detailed proof of this lemma, thus providing a sound foundation for the correctness of the fixed-point quantum search. This lemma may be of independent interest as well, since it expands the mathematical form of the recursive relation of Chebyshev polynomials of the first kind, and it also constitutes a key component in overcoming the souffle problem of quantum walk-based search algorithms, for example, robust quantum walk search on complete bipartite graphs [Phys. Rev. A 106, 052207 (2022)]. Hopefully, more applications of the lemma will be found in the future.
- [72] arXiv:2403.09519 (replaced) [pdf, ps, html, other]
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Title: Efficient tensor networks for control-enhanced quantum metrologyComments: 12+3 pages, 7 figures; improved efficiency; added variational unitary control optimization; more numerical experimentsSubjects: Quantum Physics (quant-ph)
Optimized quantum control can enhance the performance and noise resilience of quantum metrology. However, the optimization quickly becomes intractable when multiple control operations are applied sequentially. In this work, we propose efficient tensor network algorithms for optimizing strategies of quantum metrology enhanced by a long sequence of control operations. Our approach covers a general and practical scenario where the experimenter applies $N-1$ interleaved control operations between $N$ queries of the channel to estimate and uses no or bounded ancilla. Tailored to different experimental capabilities, these control operations can be generic quantum channels or variational unitary gates. Numerical experiments show that our algorithm has a good performance in optimizing the metrological strategy for as many as $N=100$ queries. In particular, our algorithm identifies a strategy that can outperform the state-of-the-art strategy when $N$ is finite but large.
- [73] arXiv:2403.14249 (replaced) [pdf, ps, other]
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Title: Direct Probe of Topology and Geometry of Quantum States on IBM QComments: 14 pages, 8 figures (updated main text and references)Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly re-constructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms, suitable for IBM quantum computers, to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for Noisy Intermediate-Scale Quantum (NISQ)-era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analysed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system.
- [74] arXiv:2403.16810 (replaced) [pdf, ps, html, other]
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Title: Holographic Gaussian Boson Sampling with Matrix Product States on 3D cQED ProcessorsSubjects: Quantum Physics (quant-ph)
We introduce quantum circuits for simulations of multi-mode state-vectors on 3D cQED processors, using matrix product state representations. The circuits are demonstrated as applied to simulations of molecular docking based on holographic Gaussian boson sampling, as illustrated for binding of a thiol-containing aryl sulfonamide ligand to the tumor necrosis factor-$\alpha$ converting enzyme receptor. We show that cQED devices with a modest number of modes could be employed to simulate multimode systems by re-purposing working modes through measurement and re-initialization. We anticipate a wide range of GBS applications could be implemented on compact 3D cQED processors analogously, using the holographic approach. Simulations on qubit-based quantum computers could be implemented analogously, using circuits that represent continuous variables in terms of truncated expansions of Fock states.
- [75] arXiv:2405.06051 (replaced) [pdf, ps, other]
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Title: Explicit decoders using quantum singular value transformationComments: 23 pages, 12 figures, 2 tablesSubjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
Recovering quantum information from a noisy quantum system is one of the central challenges in quantum information science and fundamental physics. The key to this goal is explicitly constructing a decoder. In this paper, we provide two explicit decoding quantum circuits that are both capable of recovering quantum information when a decoupling condition is satisfied, i.e., when quantum information is in principle recoverable. The decoders are constructed by using the fixed-point amplitude amplification algorithm based on the quantum singular value transformation, which significantly extends an approach by Yoshida and Kitaev in a specific noise model to general situations. We also show that the proposed decoding circuits reduce the computational cost compared to a previously known explicit decoder. Our constructions not only show an intriguing intersection between decoders and quantum algorithms but also reveal the power of an algorithmic approach to recovering quantum information.
- [76] arXiv:2405.07486 (replaced) [pdf, ps, html, other]
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Title: A Room-Temperature Solid-State Maser AmplifierTom Day, Maya Isarov, William J. Pappas, Brett C. Johnson, Hiroshi Abe, Takeshi Ohshima, Dane R. McCamey, Arne Laucht, Jarryd J. PlaSubjects: Quantum Physics (quant-ph); Instrumentation and Detectors (physics.ins-det)
Masers once represented the state-of-the-art in low noise microwave amplification technology, but eventually became obsolete due to their need for cryogenic cooling. Masers based on solid-state spin systems perform most effectively as amplifiers, since they provide a large density of spins and can therefore operate at relatively high powers. Whilst solid-state masers oscillators have been demonstrated at room temperature, continuous-wave amplification in these systems has only ever been realized at cryogenic temperatures. Here we report on a continuous-wave solid-state maser amplifier operating at room temperature. We achieve this feat using a practical setup that includes an ensemble of nitrogen-vacancy center spins in a diamond crystal, a strong permanent magnet and simple laser diode. We describe important amplifier characteristics including gain, bandwidth, compression power and noise temperature and discuss the prospects of realizing a room-temperature near-quantum-noise-limited amplifier with this system. Finally, we show that in a different mode of operation the spins can be used to cool the system noise in an external circuit to cryogenic levels, all without the requirement for physical cooling.
- [77] arXiv:2405.07613 (replaced) [pdf, ps, other]
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Title: Simulating Floquet scrambling circuits on trapped-ion quantum computersComments: 26 pages, 16 figuresSubjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
Complex quantum many-body dynamics spread initially localized quantum information across the entire system. Information scrambling refers to such a process, whose simulation is one of the promising applications of quantum computing. We demonstrate the Hayden-Preskill recovery protocol and the interferometric protocol for calculating out-of-time-ordered correlators to study the scrambling property of a one-dimensional kicked-Ising model on 20-qubit trapped-ion quantum processors. The simulated quantum circuits have a geometrically local structure that exhibits the ballistic growth of entanglement, resulting in the circuit depth being linear in the number of qubits for the entire state to be scrambled. We experimentally confirm the growth of signals in the Hayden-Preskill recovery protocol and the decay of out-of-time-ordered correlators at late times. As an application of the created scrambling circuits, we also experimentally demonstrate the calculation of the microcanonical expectation values of local operators adopting the idea of thermal pure quantum states.
- [78] arXiv:2405.13391 (replaced) [pdf, ps, html, other]
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Title: Unitary Quantum Algorithm for the Lattice-Boltzmann MethodDavid Wawrzyniak, Josef Winter, Steffen Schmidt, Thomas Indinger, Uwe Schramm, Christian Janßen, Nikolaus A. AdamsSubjects: Quantum Physics (quant-ph)
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium within a single time step. Our quantum algorithm enables the computation of multiple time steps in the linearized case, specifically for solving the advection-diffusion equation, before necessitating a full state measurement. Moreover, our formulation can be extended to compute the non-linear equilibrium distribution function for a single time step prior to measurement, utilizing the measurement as an essential algorithmic step. However, in the non-linear case, a classical postprocessing step is necessary for computing the moments of the distribution function. We validate our algorithm by solving the one dimensional advection-diffusion of a Gaussian hill. Our results demonstrate that our quantum algorithm captures non-linearity.
- [79] arXiv:2405.15022 (replaced) [pdf, ps, html, other]
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Title: Evidence of the quantum-optical nature of high-harmonic generationDavid Theidel, Viviane Cotte, René Sondenheimer, Viktoriia Shiriaeva, Marie Froidevaux, Vladislav Severin, Philip Mosel, Adam Merdji-Larue, Sven Fröhlich, Kim-Alessandro Weber, Uwe Morgner, Milutin Kovacev, Jens Biegert, Hamed MerdjiComments: 39 pages, 11 figuresSubjects: Quantum Physics (quant-ph)
High-harmonic generation is a light up-conversion process occurring in a strong laser field, leading to coherent bursts of extreme ultrashort broadband radiation [1]. As a new perspective, we propose that ultrafast strong-field electronic or photonic processes such as high-harmonic generation can potentially generate non-classical states of light well before the decoherence of the system occurs [2, 3]. This could address fundamental challenges in quantum technology such as scalability, decoherence or the generation of massively entangled states [4]. Here, we report experimental evidence of the non-classical nature of the harmonic emission in several semiconductors excited by a femtosecond infrared laser. By investigating single- and double beam intensity cross-correlation [5], we measure characteristic, non-classical features in the single photon statistics. We observe two-mode squeezing in the generated harmonic radiation, which depends on the laser intensity that governs the transition from Super-Poissonian to Poissonian photon statistics. The measured violation of the Cauchy-Schwarz inequality realizes a direct test of multipartite entanglement in high-harmonic generation [6]. This result is supported by the theory of multimodal detection and the Hamiltonian from which the effective squeezing modes of the harmonics can be derived [7, 8]. With this work, we show experimentally that high-harmonic generation is a new quantum bosonic platform that intrinsically produces non-classical states of light with unique features such as multipartite broadband entanglement or multimode squeezing. The source operates at room temperature using standard semiconductors and a standard commercial fiber laser, opening new routes for the quantum industry, such as optical quantum computing, communication and imaging.
- [80] arXiv:2405.17021 (replaced) [pdf, ps, html, other]
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Title: Truncated Modular Exponentiation Operators: A Strategy for Quantum FactoringComments: 45 pages, 33 figures. Added several figures that quantify the truncation studiesSubjects: Quantum Physics (quant-ph)
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. I propose a method for constructing the ME operators that relies upon the simple observation that the work register starts in state $\vert 1 \rangle$. Therefore, we do not have to create an ME operator $U$ that accepts a general input, but rather, one that takes an input from the periodic sequence of states $\vert f(x) \rangle$ for $x \in \{0, 1, \cdots, r-1\}$, where $f(x)$ is the ME function with period $r$. The operator $U$ can be partitioned into $r$ levels, where the gates in level $x \in \{0, 1, \cdots, r-1\}$ increment the state $\vert f(x) \rangle$ to the state $\vert f(x+1) \rangle$. The gates below $x$ do not affect the state $\vert f(x+1) \rangle$. The obvious problem with this method is that it is self-defeating: If we knew the operator $U$, then we would know the period $r$ of the ME function, and there would be no need for Shor's algorithm. I show, however, that the ME operators are very forgiving, and truncated approximate forms in which levels have been omitted are able to extract factors just as well as the exact operators. I demonstrate this by factoring the numbers $N = 21, 33, 35, 143, 247$ by using less than half the requisite number of levels in the ME operators. This procedure works because the method of continued fractions only requires an approximate phase value. This is the basis for a factorization strategy in which we fill the circuits for the ME operators with more and more gates, and the correlations between the various composite operators $U^p$ (where $p$ is a power of two) compensate for the missing levels.
- [81] arXiv:2405.20382 (replaced) [pdf, ps, html, other]
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Title: Dipole-dipole interactions mediated by a photonic flat bandComments: 18 pages, 6 figuresSubjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
Flat bands (FBs) are energy bands with zero group velocity, which in electronic systems were shown to favor strongly correlated phenomena. Indeed, a FB can be spanned with a basis of strictly localized states, the so called "compact localized states" (CLSs), which are yet generally non-orthogonal. Here, we study emergent dipole-dipole interactions between emitters dispersively coupled to the photonic analogue of a FB, a setup within reach in state-of the-art experimental platforms. We show that the strength of such photon-mediated interactions decays exponentially with distance with a characteristic localization length which, unlike typical behaviours with standard bands, saturates to a finite value as the emitter's energy approaches the FB. Remarkably, we find that the localization length grows with the overlap between CLSs according to an analytically-derived universal scaling law valid for a large class of FBs both in 1D and 2D. Using giant atoms (non-local atom-field coupling) allows to tailor interaction potentials having the same shape of a CLS or a superposition of a few of these.
- [82] arXiv:2406.01590 (replaced) [pdf, ps, html, other]
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Title: Generalized phase estimation in noisy quantum gatesComments: 11 pages, 5 figuresSubjects: Quantum Physics (quant-ph)
We examine metrological scenarios where the parameter of interest is encoded onto a quantum state through the action of a noisy quantum gate and investigate the ultimate bound to precision by analyzing the behaviour of the Quantum Fisher Information (QFI). We focus on qubit gates and consider the possibility of employing successive applications of the gate. We go beyond the trivial case of unitary gates and characterize the robustness of the metrological procedure introducing noise in the performed quantum operation, looking at how this affects the QFI at different steps (gate applications). We model the dephasing and tilting noise affecting qubit rotations as classical fluctuations governed by a Von Mises-Fisher distribution. Compared to the noiseless case, in which the QFI grows quadratically with the number of steps, we observe a non monotonic behavior, and the appearance of a maximum in the QFI, which defines the ideal number of steps that should be performed in order to precisely characterize the action of the gate.
- [83] arXiv:2205.12325 (replaced) [pdf, ps, html, other]
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Title: Perturbation Theory and the Sum of SquaresComments: 15 pages; v2 minor corrections and clarifications, more consideration of number conservation; v3, typo correctionsSubjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
The sum-of-squares (SoS) hierarchy is a powerful technique based on semi-definite programming that can be used for both classical and quantum optimization problems. This hierarchy goes under several names; in particular, in quantum chemistry it is called the reduced density matrix (RDM) method. We consider the ability of this hierarchy to reproduce weak coupling perturbation theory for three different kinds of systems: spin (or qubit) systems, bosonic systems (the anharmonic oscillator), and fermionic systems with quartic interactions. For such fermionic systems, we show that degree-$4$ SoS (called $2$-RDM in quantum chemsitry) does not reproduce second order perturbation theory but degree-$6$ SoS ($3$-RDM) does (and we conjecture that it reproduces third order perturbation theory). Indeed, we identify a fragment of degree-$6$ SoS which can do this, which may be useful for practical quantum chemical calculations as it may be possible to implement this fragment with less cost than the full degree-$6$ SoS. Remarkably, this fragment is very similar to one studied by Hastings and O'Donnell for the Sachdev-Ye-Kitaev (SYK) model.
- [84] arXiv:2401.10913 (replaced) [pdf, ps, html, other]
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Title: Symmetry-induced higher-order exceptional points in two dimensionsJournal-ref: Phys. Rev. Research 6, 023205 (2024)Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics); Quantum Physics (quant-ph)
Exceptional points of order $n$ (EP$n$s) appear in non-Hermitian systems as points where the eigenvalues and eigenvectors coalesce. They emerge if $2(n-1)$ real constraints are imposed, such that EP2s generically appear in two dimensions (2D). Local symmetries have been shown to reduce this number of constraints. In this work, we provide a complete characterization of the appearance of symmetry-induced higher-order EPs in 2D parameter space. We find that besides EP2s only EP3s, EP4s, and EP5s can be stabilized in 2D. Moreover, these higher-order EPs must always appear in pairs with their dispersion determined by the symmetries. Upon studying the complex spectral structure around these EPs, we find that depending on the symmetry, EP3s are accompanied by EP2 arcs, and two- and three-level open Fermi structures. Similarly, EP4s and closely related EP5s, which arise due to multiple symmetries, are accompanied by exotic EP arcs and open Fermi structures. For each case, we provide an explicit example. We also comment on the topological charge of these EPs, and discuss similarities and differences between symmetry-protected higher-order EPs and EP2s.
- [85] arXiv:2404.06092 (replaced) [pdf, ps, html, other]
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Title: Analytic thermodynamic properties of the Lieb-Liniger gasComments: 55 pages, 9 figures; minor revisions in v2 in response to referee's commentsSubjects: Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact repulsive interactions. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics -- thanks to its integrability and possible experimental realization using, e.g., ensembles of ultracold bosonic atoms confined to quasi-1D geometries. The thermodynamics of the uniform Lieb-Liniger gas can be obtained numerically using the exact thermal Bethe ansatz (TBA) method, first derived in 1969 by Yang and Yang. However, the TBA numerical calculations do not allow for the in-depth understanding of the underlying physical mechanisms that govern the thermodynamic behavior of the Lieb-Liniger gas at finite temperature. Our work is then motivated by the insights that emerge naturally from the transparency of closed-form analytic results, which are derived here in six different regimes of the gas and which exhibit an excellent agreement with the TBA numerics. Our findings can be further adopted for characterising the equilibrium properties of inhomogeneous (e.g., harmonically trapped) 1D Bose gases within the local density approximation and for the development of improved hydrodynamic theories, allowing for the calculation of breathing mode frequencies which depend on the underlying thermodynamic equation of state. Our analytic approaches can be applied to other systems including impurities in a quantum bath, liquid helium-4, and ultracold Bose gas mixtures.
- [86] arXiv:2405.05973 (replaced) [pdf, ps, html, other]
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Title: Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma(36\times3)$Comments: 15 pages, 11 Figures, 6 TablesSubjects: High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)
We construct the primitive gate set for the digital quantum simulation of the 108-element $\Sigma(36\times3)$ group. This is the first time a nonabelian crystal-like subgroup of $SU(3)$ has been constructed for quantum simulation. The gauge link registers and necessary primitives -- the inversion gate, the group multiplication gate, the trace gate, and the $\Sigma(36\times3)$ Fourier transform -- are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture.
- [87] arXiv:2405.09005 (replaced) [pdf, ps, html, other]
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Title: Cons-training tensor networksComments: v2: mostly improved Fig 1 and 13 for clarity, improved exposition of ideas, and fixed a couple of transcription bugs in the pseudo algo. 3Subjects: Numerical Analysis (math.NA); Machine Learning (cs.LG); Quantum Physics (quant-ph)
In this study, we introduce a novel family of tensor networks, termed \textit{constrained matrix product states} (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures. These tensor networks are particularly tailored for modeling distributions with support strictly over the feasible space, offering benefits such as reducing the search space in optimization problems, alleviating overfitting, improving training efficiency, and decreasing model size. Central to our approach is the concept of a quantum region, an extension of quantum numbers traditionally used in U(1) symmetric tensor networks, adapted to capture any linear constraint, including the unconstrained scenario. We further develop a novel canonical form for these new MPS, which allow for the merging and factorization of tensor blocks according to quantum region fusion rules and permit optimal truncation schemes. Utilizing this canonical form, we apply an unsupervised training strategy to optimize arbitrary objective functions subject to discrete linear constraints. Our method's efficacy is demonstrated by solving the quadratic knapsack problem, achieving superior performance compared to a leading nonlinear integer programming solver. Additionally, we analyze the complexity and scalability of our approach, demonstrating its potential in addressing complex constrained combinatorial optimization problems.