Quantum Physics (quant-ph)

Abstract: The counter diabatic (CD) driving has attracted much attention for suppressing non-adiabatic transition in quantum annealing (QA). However, it can be intractable to construct the CD driving in the actual experimental setup due to the non-locality of the CD dariving Hamiltonian and necessity of exact diagonalization of the QA Hamiltonian in advance. In this paper, using the mean field (MF) theory, we propose a general method to construct an approximated CD driving term consisting of local operators. We can efficiently construct the MF approximated CD (MFCD) term by solving the MF dynamics of magnetization using a classical computer. As an example, we numerically perform QA with MFCD driving for the spin glass model with transverse magnetic fields. We numerically show that the MF dynamics with MFCD driving is equivalent to the solution of the self-consistent equation in MF theory. Also, we clarify that a ground state of the spin glass model with transverse magnetic field can be obtained with high fidelity compared to the conventional QA without the CD driving. Moreover, we experimentally demonstrate our method by using a D-wave quantum annealer and obtain the experimental result supporting our numerical simulation.

Abstract: The non-Hermitian model exhibits counter-intuitive phenomena which are not observed in the Hermitian counterparts. To probe the competition between non-Hermitian and Hermitian interacting components of the Hamiltonian, we focus on a system containing non-Hermitian XY spin chain and Hermitian Kaplan-Shekhtman-Entin-Aharony (KSEA) interactions along with the transverse magnetic field. We show that the non-Hermitian model can be an effective Hamiltonian of a Hermitian XX spin-1/2 with KSEA interaction and a local magnetic field that interacts with local and non-local reservoirs. The analytical expression of the energy spectrum divides the system parameters into two regimes -- in one region, the strength of Hermitian KSEA interactions dominates over the imaginary non-Hermiticity parameter while in the other, the opposite is true. In the former situation, we demonstrate that the nearest-neighbor entanglement and its derivative can identify quantum critical lines with the variation of the magnetic field. In this domain, we determine a surface where the entanglement vanishes, similar to the factorization surface, known in the Hermitian case. On the other hand, when non-Hermiticity parameters dominate, we report the exceptional and critical points where the energy gap vanishes and illustrate that bipartite entanglement is capable of detecting these transitions as well. Going beyond this scenario, when the ground state evolves after a sudden quench with the transverse magnetic field, both rate function and the fluctuation of bipartite entanglement quantified via its second moment can detect critical lines generated without quenching dynamics.

Abstract: Recently, it has been shown that locally randomized measurements can be employed to get partial transpose moments of a density matrix [Elben A., {\it et al.} Phys. Rev. Lett. {\bf 125}, 200501 (2020)]. Consequently, two general entanglement detection methods were proposed based on partial transpose moments of a density matrix [Yu X-D., {\it et al.} Phys. Rev. Lett. {\bf 127}, 060504 (2021)]. In this context, a natural question arises that how partial transpose moments are related with entanglement and with well known idea of principal minors. In this work, we analytically demonstrate that for qubit-qubit quantum systems, partial transpose moments can be expressed as simple functions of principal minors. We expect this relation to exist for every bipartite quantum systems. In addition, we have extended the idea of PT-moments for tripartite qubit systems and have shown that PT-moments can only detect the whole range of being NPT for $GHZ$ and $W$ states mixed with white noise.

Abstract: We present a null witness, based on equality due to linear independence, of the dimension of a quantum system, discriminating real, complex and classical spaces. The witness involves only a single measurement with sufficiently many outcomes and prepared input states. In addition, for intermediate dimensions, the witness bounds saturate for a family of equiangular tight frames including symmetric informationally complete positive operator valued measures. Such a witness requires a minimum of resources, being robust against many practical imperfections. We also discuss errors due to finite statistics.

Abstract: Thermometry is a fundamental parameter estimation problem which is crucial in the development process of natural sciences. One way to solve this problem is to the extensive used local thermometry theory, which makes use of the classical and quantum Cram\'er-Rao bound as benchmarks of thermometry precision. However, such a thermometry theory can only be used for decreasing temperature fluctuations around a known temperature value and hardly tackle the precision thermometry problem over a wide temperature range. For this reason, we derive two basic bounds on thermometry precision in the global setting and further show their thermometry performance by two specific applications, i.e., noninteracting spin-1/2 gas and a general N-level thermal equilibrium quantum probe.

Abstract: Quantum coherence will undoubtedly play a fundamental role in understanding of the dynamics of quantum many-body systems, thereby to reveal its genuine contribution is of great importance. In this paper, we specialize our discussions to the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied by Fisher zeros and the rate function of Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs which are independent of equilibrium quantum critical point. We also find that Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work sheds new light on the fundamental connection between quantum critical phenomena and quantum coherence.

Abstract: The optical cat state, known as the superposition of coherent states, has broad applications in quantum computation and quantum metrology. Increasing the number of optical cat states is crucial to implement complex quantum information tasks based on them. Here, we prepare two optical cat states simultaneously based on a nondegenerate optical parametric amplifier. By subtracting one photon from each of two squeezed vacuum states, two odd cat states with orthogonal superposition direction in phase space are prepared simultaneously, which have similar fidelity of 60% and amplitude of 1.2. Compared with the traditional method to generate two odd optical cat states based on two degenerate optical parametric amplifiers, only one nondegenerate optical parametric amplifier is applied in our experiment, which saves half of the quantum resource of nonlinear cavities. The presented results make a step toward preparing the four-component cat state, which has potential applications in fault-tolerant quantum computation.

Abstract: We study the role of topology in governing deep thermalization, the relaxation of a local subsystem towards a maximally-entropic, uniform distribution of post-measurement states, upon observing the complementary subsystem in a local basis. Concretely, we focus on a class of (1+1)d systems exhibiting `maximally-chaotic' dynamics, and consider how the rate of the formation of such a universal wavefunction distribution depends on boundary conditions of the system. We find that deep thermalization is achieved exponentially quickly in the presence of either periodic or open boundary conditions; however, the rate at which this occurs is twice as fast for the former than for the latter. These results are attained analytically using the calculus of integration over unitary groups, and supported by extensive numerical simulations. Our findings highlight the nonlocal nature of deep thermalization, and clearly illustrates that the physics underlying this phenomenon goes beyond that of standard quantum thermalization, which only depends on the net build-up of entanglement between a subsystem and its complement.

Abstract: We put forward four schemes of coupled-qubit quantum Otto machine, a generalization of the single-qubit quantum Otto machine, based on work and heat transfer between an internal system consisting of a coupled pair of qubits and an external environment consisting of two heat baths and two work storages. The four schemes of our model are defined by the positions of attaching the heat baths, which play a key role in the power of the coupled-qubit engine. Firstly, for the single-qubit heat engine, we find a maximum-power relation, and the fact that its efficiency at the maximum power is equal to the Otto efficiency, which is greater than the Curzon-Ahlborn efficiency. Second, we compare the coupled-qubit engines to the single-qubit one from the point of view of achieving the maximum power based on the same energy-level change for work production, and find that the coupling between the two qubits can lead to greater powers but the system efficiency at the maximum power is lower than the single-qubit system's efficiency and the Curzon-Ahlborn efficiency.

Abstract: In this work, we study the phenomena of quantum interference assisted magnon blockade and magnon antibunching in a weakly interacting hybrid ferromagnet-superconductor system. The magnon excitations in two yttrium iron garnet spheres are indirectly coupled to a superconducting qubit through microwave cavity modes of two mutually perpendicular cavities. We find that when one of the magnon mode is driven by a weak optical field, the destructive interference between more than two distinct transition pathways restricts simultaneous excitation of two magnons. We analyze the magnon correlations in the driven magnon mode for the case of zero detunings as well as finite detunings of the magnon modes and the qubit. We show that the magnon antibunching can be tuned by changing the magnon-qubit coupling strength ratio and the driving detuning. Our work proposes a possible scheme which have significant role in the construction of single magnon generating devices.

Abstract: The heralded generation of entangled states underpins many photonic quantum technologies. As quantum error correction thresholds are determined by underlying physical noise mechanisms, a detailed and faithful characterization of resource states is required. Non-computational leakage, e.g. more than one photon occupying a dual-rail encoded qubit, is an error not captured by standard forms of state tomography, which postselect on photons remaining in the computational subspace. Here we use the continuous-variable (CV) formalism and first quantized state representation to develop a simulation framework that reconstructs photonic quantum states in the presence of partial distinguishability and resulting non-computational leakage errors. Using these tools, we analyze a variety of Bell state generation circuits and find that the five photon discrete Fourier transform (DFT) Bell state generation scheme [Phys Rev. Lett. 126 23054 (2021)] is most robust to such errors for near-ideal photons. Through characterization of a photonic entangling gate, we demonstrate how leakage errors prevent a modular characterization of concatenated gates using current tomographical procedures. Our work is a necessary step in revealing the true noise models that must be addressed in fault-tolerant photonic quantum computing architectures.

Abstract: The present study investigates the reliability of functioning systems that depend on quantum coherence. In contrast to the conventional notion of reliability in industry and technology, which is evaluated using probabilistic measurements of binary logical variables, quantum reliability is grounded in the quantum probability amplitude, or wave function, due to the interference between different system trajectories. A system of quantum storage with a fault-tolerance structure is presented to illustrate the definition and calculation of quantum reliability. Our findings reveal that quantum coherence alters the relationship between a system's reliability and that of its subsystems, compared to classical cases. This effect is particularly relevant for quantum complexes with multiple interacting subsystems that require a precise operation.

Abstract: Gaussian quantum channels are well understood and have many applications, e.g., in Quantum Information Theory and in Quantum Optics. For more general quantum channels one can in general use semiclassical approximations or perturbation theory, but it is not easy to judge the accuracy of such methods. We study a relatively simple model case, where the quantum channel is generated by a Lindblad equation where one of the Lindblad operators is a multiple of the internal Hamiltonian, and therefore the channel is not Gaussian. For this model we can compute the characteristic function of the action of the channel on a Gaussian state explicitly and we can as well derive a representation of the propagator in an integral form. This allows us to compare the exact results with semiclassical approximations and perturbation theory and evaluate their accuracy. We finally apply these results to the study of the evolution of the von Neumann entropy of a state.

Abstract: In this paper, we propose a quantum algorithm to solve the unit commitment (UC) problem at least cubically faster than existing classical approaches. This is accomplished by calculating the energy transmission costs using the HHL algorithm inside a QAOA routine. We verify our findings experimentally using quantum circuit simulators in a small case study. Further, we postulate the applicability of the concepts developed for this algorithm to be used for a large class of optimization problems that demand solving a linear system of equations in order to calculate the cost function for a given solution.

Abstract: Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model for quantum neural computing using (classically-controlled) single-qubit operations and measurements on real-world quantum systems with naturally occurring environment-induced decoherence, which greatly reduces the difficulties of physical implementations. Our model circumvents the problem that the state-space size grows exponentially with the number of neurons, thereby greatly reducing memory requirements and allowing for fast optimization with traditional optimization algorithms. We benchmark our model for handwritten digit recognition and other nonlinear classification tasks. The results show that our model has an amazing nonlinear classification ability and robustness to noise. Furthermore, our model allows quantum computing to be applied in a wider context and inspires the earlier development of a quantum neural computer than standard quantum computers.

Abstract: Consider a free Schr\"odinger particle inside an interval with walls characterized by the Dirichlet boundary condition. Choose a parabola as the normalized state of the particle that satisfies this boundary condition. To calculate the variance of the Hamiltonian in that state, one needs to calculate the mean value of the Hamiltonian and that of its square. If one uses the standard formula to calculate these mean values, one obtains both results without difficulty, but the variance unexpectedly takes an imaginary value. If one uses the same expression to calculate these mean values but first writes the Hamiltonian and its square in terms of their respective eigenfunctions and eigenvalues, one obtains the same result as above for the mean value of the Hamiltonian but a different value for its square (in fact, it is not zero); hence, the variance takes an acceptable value. From whence do these contradictory results arise? The latter paradox has been presented in the literature as an example of a problem that can only be properly solved by making use of certain fundamental concepts within the general theory of linear operators in Hilbert spaces. Here, we carefully review those concepts and apply them in a detailed way to resolve the paradox. Our results are formulated within the natural framework of wave mechanics, and to avoid inconveniences that the use of Dirac's symbolic formalism could bring, we avoid the use of that formalism throughout the article. In addition, we obtain a resolution of the paradox in an entirely formal way without addressing the restrictions imposed by the domains of the operators involved. We think that the content of this paper will be useful to undergraduate and graduate students as well as to their instructors.

Abstract: One of the major benefits of quantum computing is the potential to resolve complex computational problems faster than can be done by classical methods. There are many prototype-based clustering methods in use today, and the selection of the starting nodes for the center points is often done randomly. Clustering often suffers from accepting a local minima as a valid solution when there are possibly better solutions. We will present the results of a study to leverage the benefits of quantum computing for finding better starting centroids for prototype-based clustering.

Abstract: Information Reconciliation is an essential part of Quantum Key distribution protocols that closely resembles Slepian-Wolf coding. The application of nonbinary LDPC codes in the Information Reconciliation stage of a high-dimensional discrete-variable Quantum Key Distribution setup is proposed. We model the quantum channel using a $q$-ary symmetric channel over which qudits are sent. Node degree distributions optimized via density evolution for the Quantum Key Distribution setting are presented, and we show that codes constructed using these distributions allow for efficient reconciliation of large-alphabet keys.

Abstract: In this theoretical investigation, we study the effectiveness of a protocol that incorporates periodic quantum resetting to prepare ground states of frustration-free parent Hamiltonians. This protocol uses a steering Hamiltonian that enables local coupling between the system and ancillary degrees of freedom. At periodic intervals, the ancillary system is reset to its initial state. For infinitesimally short reset times, the dynamics can be approximated by a Lindbladian whose steady state is the target state. For finite reset times, however, the spin chain and the ancilla become entangled between reset operations. To evaluate the performance of the protocol, we employ Matrix Product State simulations and quantum trajectory techniques, focusing on the preparation of the spin-1 Affleck-Kennedy-Lieb-Tasaki state. Our analysis considers convergence time, fidelity, and energy evolution under different reset intervals. Our numerical results show that ancilla system entanglement is essential for faster convergence. In particular, there exists an optimal reset time at which the protocol performs best. Using a simple approximation, we provide insights into how to optimally choose the mapping operators applied to the system during the reset procedure. Furthermore, the protocol shows remarkable resilience to small deviations in reset time and dephasing noise. Our study suggests that stroboscopic maps using quantum resetting may offer advantages over alternative methods, such as quantum reservoir engineering and quantum state steering protocols, which rely on Markovian dynamics.

Abstract: We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of $N$ spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime $N\gg 1$, assuming that the qubit-bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behavior is captured by an analytical approximation that makes use of the property $N\gg 1$ to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.

Abstract: We present a detailed scheme for the implementation of $\mathbb{Z}_2$ gauge theories with dynamical bosonic matter using analog quantum simulators based on crystals of trapped ions. We introduce a versatile toolbox based on a state-dependent parametric excitation, which can be implemented using different interactions that couple the ions' internal qubit states to their motion, and induces a tunneling of the vibrational excitations of the crystal mediated by the trapped-ion qubits. To evaluate the feasibility of this toolbox, we perform numerical simulations of the considered schemes using realistic experimental parameters. This building block, when implemented with a single trapped ion, corresponds to a minimal $\mathbb{Z}_2$ gauge theory on a synthetic link where the qubit resides, playing the role of the gauge field. The vibrational excitations of the ion along different trap axes mimic the dynamical matter fields carrying a $\mathbb{Z}_2$ charge. We discuss how to generalise this minimal case to more complex settings by increasing the number of ions. We describe various possibilities which allow us to move from a single $\mathbb{Z}_2$ plaquette to full $\mathbb{Z}_2$ gauge chains. We present analytical expressions for the gauge-invariant dynamics and confinement, which are benchmarked using matrix product state simulations.

Abstract: We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are not sufficient to construct an informationally complete positive operator-valued measurement (IC-POVM) for pure states. We demonstrate our method using a binary tree structure, providing an algorithmic path for implementation. The performance of the method is evaluated through numerical simulations, showcasing its effectiveness for quantum state estimation.

Abstract: Quantum computation is expected to accelerate certain computational task over classical counterpart. Its most primitive advantage is its ability to sample from classically intractable probability distributions. A promising approach to make use of this fact is the so-called quantum-enhanced Markov chain Monte Carlo (MCMC) [D. Layden, et al., arXiv:2203.12497 (2022)] which uses outputs from quantum circuits as the proposal distributions. In this work, we propose the use of Quantum Alternating Operator Ansatz (QAOA) for quantum-enhanced MCMC and provide a strategy to optimize its parameter to improve convergence speed while keeping its depth shallow. The proposed QAOA-type circuit is designed to satisfy the specific constraint which quantum-enhanced MCMC requires with arbitrary parameters. Through our extensive numerical analysis, we find a correlation in certain parameter range between an experimentally measurable value, acceptance rate of MCMC, and the spectral gap of the MCMC transition matrix, which determines the convergence speed. This allows us to optimize the parameter in the QAOA circuit and achieve quadratic speedup in convergence. Since MCMC is used in various areas such as statistical physics and machine learning makes, this work represents an important step toward realizing practical quantum advantage with currently available quantum computers through quantum-enhanced MCMC.

Abstract: Holistic benchmarks for quantum computers are essential for testing and summarizing the performance of quantum hardware. However, holistic benchmarks -- such as algorithmic or randomized benchmarks -- typically do not predict a processor's performance on circuits outside the benchmark's necessarily very limited set of test circuits. In this paper, we introduce a general framework for building predictive models from benchmarking data using capability models. Capability models can be fit to many kinds of benchmarking data and used for a variety of predictive tasks. We demonstrate this flexibility with two case studies. In the first case study, we predict circuit (i) process fidelities and (ii) success probabilities by fitting error rates models to two kinds of volumetric benchmarking data. Error rates models are simple, yet versatile capability models which assign effective error rates to individual gates, or more general circuit components. In the second case study, we construct a capability model for predicting circuit success probabilities by applying transfer learning to ResNet50, a neural network trained for image classification. Our case studies use data from cloud-accessible quantum computers and simulations of noisy quantum computers.

Abstract: We show that chemically-accurate potential energy surfaces (PESs) can be generated from quantum computers by measuring the density along an adiabatic transition between different molecular geometries. In lieu of using phase estimation, the energy is evaluated by performing line-integration using the inverted TDDFT Kohn-Sham potential obtained from the time-varying densities. The accuracy of this method depends on the validity of the adiabatic evolution itself and the potential inversion process (which is theoretically exact but can be numerically unstable), whereas total evolution time is the defining factor for the precision of phase estimation. We examine the method with a one-dimensional system of two electrons for both the ground and first triplet state in first quantization, as well as the ground state of three- and four- electron systems in second quantization. It is shown that few accurate measurements can be utilized to obtain chemical accuracy across the full potential energy curve, with shorter propagation time than may be required using phase estimation for a similar accuracy. We also show that an accurate potential energy curve can be calculated by making many imprecise density measurements (using few shots) along the time evolution and smoothing the resulting density evolution. We discuss how one can generate full PESs using either sparse grid representations or machine learning density functionals where it is known that training the functional using the density (along with the energy) generates a more transferable functional than only using the energy. Finally, it is important to note that the method is able to classically provide a check of its own accuracy by comparing the density resulting from a time-independent Kohn-Sham calculation using the inverted potential, with the measured density.