arXiv subjects

Nobuyuki Yoshioka

Publications and source records attributed to Nobuyuki Yoshioka.

At least 55 records · Page 3Linked to original sources

arXiv2024

Universal cost bound of quantum error mitigation based on quantum estimation theory

We present a unified approach to analyzing the cost of various quantum error mitigation methods on the basis of quantum estimation theory. By analyzing the quantum Fisher information matrix of a virtual quantum circuit that effectively represents the operations of quantum error mitigation methods, we derive for a generic layered quantum circuit under a wide class of Markovian noise that, unbiased estimation of an observable encounters an exponential growth with the circuit depth in the lower bound on the measurement cost. Under the global depolarizing noise, we in particular find that the bound can be asymptotically saturated by merely rescaling the measurement results. Moreover, we prove for random circuits with local noise that the cost grows exponentially also with the qubit count. Our numerical simulations support the observation that, even if the circuit has only linear connectivity, such as the brick-wall structure, each noise channel converges to the global depolarizing channel with its strength growing exponentially with the qubit count. This not only implies the exponential growth of cost both with the depth and qubit count, but also validates the rescaling technique for sufficiently deep quantum circuits. Our results contribute to the understanding of the physical limitations of quantum error mitigation and offer a new criterion for evaluating the performance of quantum error mitigation techniques.

quant-ph↗

arXiv2023

Balancing error budget for fermionic k-RDM estimation

The reduced density matrix (RDM) is crucial in quantum many-body systems for understanding physical properties, including all local physical quantity information. This study aims to minimize various error constraints that causes challenges in higher-order RDMs estimation in quantum computing. We identify the optimal balance between statistical and systematic errors in higher-order RDM estimation in particular when cumulant expansion is used to suppress the sample complexity. Furthermore, we show via numerical demonstration of quantum subspace methods for one and two dimensional Fermi Hubbard model that, biased yet efficient estimations better suppress hardware noise in excited state calculations. Our work paves a path towards cost-efficient practical quantum computing that in reality is constrained by multiple aspects of errors.

quant-ph↗

arXiv2023

Subspace methods for electronic structure simulations on quantum computers

Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrodinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the Schrodinger equation into an eigenvalue problem determined by measurements carried out on a quantum device. The eigenvalue problem is then solved on a classical computer, yielding approximations to ground- and excited-state energies and wavefunctions. QSMs are examples of hybrid quantum-classical methods, where a quantum device supported by classical computational resources is employed to tackle a problem. QSMs are rapidly gaining traction as a strategy to simulate electronic wavefunctions on quantum computers, and thus their design, development, and application is a key research field at the interface between quantum computation and electronic structure. In this review, we provide a self-contained introduction to QSMs, with emphasis on their application to the electronic structure of molecules. We present the theoretical foundations and applications of QSMs, and we discuss their implementation on quantum hardware, illustrating the impact of noise on their performance.

quant-ph↗

arXiv2023

Virtual quantum error detection

Quantum error correction and quantum error detection necessitate syndrome measurements to detect errors. Performing syndrome measurements for each stabilizer generator can be a significant overhead, considering the fact that the readout fidelity in the current quantum hardware is generally lower than gate fidelity. Here, by generalizing a quantum error mitigation method known as symmetry expansion, we propose a protocol called virtual quantum error detection (VQED). This method virtually allows for evaluating computation results corresponding to post-selected quantum states obtained through quantum error detection during circuit execution, without implementing syndrome measurements. Unlike conventional quantum error detection, which requires the implementation of Hadamard test circuits for each stabilizer generator, our VQED protocol can be performed with a constant depth shallow quantum circuit with an ancilla qubit, irrespective of the number of stabilizer generators. Furthermore, for some simple error models, the computation results obtained using VQED are robust against the noise that occurred during the operation of VQED, and our method is fully compatible with other error mitigation schemes, enabling further improvements in computation accuracy and facilitating high-fidelity quantum computing.

quant-ph↗

arXiv2023

Work extractability from energy eigenstates under optimized local operations

We examine the relationship between the second law of thermodynamics and the energy eigenstates of quantum many-body systems that undergo cyclic unitary evolution. Using a numerically optimized control protocol, we analyze how the work extractability is affected by the integrability of the system. Our findings reveal that, in nonintegrable systems the number of work-extractable energy eigenstates converges to zero, even when the local control operations are optimized. In contrast, in integrable systems, there are exponentially many eigenstates from which positive work can be extracted, regardless of the locality of the control operations. We numerically demonstrate that such a strikingly different behavior can be attributed to the number of athermal energy eigenstates. Our results provide insights into the foundations of the second law of thermodynamics in isolated quantum many-body systems, which are expected to contribute to the development of quantum many-body heat engines.

quant-ph↗

arXiv2023

Nonlinearity-induced topological phase transition characterized by the nonlinear Chern number

As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The bulk-boundary correspondence guarantees the emergence of gapless boundary modes in a topological system whose bulk exhibits nonzero topological invariants. Although some recent studies have suggested a possible extension of the notion of topology to nonlinear systems such as photonics and electrical circuits, the nonlinear counterpart of topological invariant has not yet been understood. Here, we propose the nonlinear extension of the Chern number based on the nonlinear eigenvalue problems in two-dimensional systems and reveal the bulk-boundary correspondence beyond the weakly nonlinear regime. Specifically, we find the nonlinearity-induced topological phase transitions, where the existence of topological edge modes depends on the amplitude of oscillatory modes. We propose and analyze a minimal model of a nonlinear Chern insulator whose exact bulk solutions are analytically obtained and indicate the amplitude dependence of the nonlinear Chern number, for which we confirm the nonlinear counterpart of the bulk-boundary correspondence in the continuum limit. Thus, our result reveals the existence of genuinely nonlinear topological phases that are adiabatically disconnected from the linear regime, showing the promise for expanding the scope of topological classification of matter towards the nonlinear regime.

cond-mat.mes-hall↗

arXiv2023

Leveraging hardware-control imperfections for error mitigation via generalized quantum subspace

In the era of quantum computing without full fault-tolerance, it is essential to suppress noise effects via the quantum error mitigation techniques to enhance the computational power of the quantum devices. One of the most effective noise-agnostic error mitigation schemes is the generalized quantum subspace expansion (GSE) method, which unifies various mitigation algorithms under the framework of the quantum subspace expansion. Specifically, the fault-subspace method, a subclass of GSE method, constructs an error-mitigated quantum state with copies of quantum states with different noise levels. However, from the experimental aspect, it is nontrivial to determine how to reliably amplify the noise so that the error in the simulation result is efficiently suppressed. In this work, we explore the potential of the fault-subspace method by leveraging the hardware-oriented noise: intentional amplification of the decoherence, noise boost by insertion of identity, making use of crosstalk, and probabilistic implementation of noise channel. We demonstrate the validity of our proposals via both numerical simulations with the noise parameters reflecting those in quantum devices available via IBM Quantum, and also experiments performed therein.

quant-ph↗

arXiv2023

Deep reinforcement learning for preparation of thermal and prethermal quantum states

We propose a method based on deep reinforcement learning that efficiently prepares a quantum many-body pure state in thermal or prethermal equilibrium. The main physical intuition underlying the method is that the information on the equilibrium states can be efficiently encoded/extracted by focusing on only a few local observables, relying on the typicality of equilibrium states. Instead of resorting to the expensive preparation protocol that adopts global features such as the quantum state fidelity, we show that the equilibrium states can be efficiently prepared only by learning the expectation values of local observables. We demonstrate our method by preparing two illustrative examples: Gibbs ensembles in non-integrable systems and generalized Gibbs ensembles in integrable systems. Pure states prepared solely from local observables are numerically shown to successfully encode the macroscopic properties of the equilibrium states. Furthermore, we find that the preparation errors, with respect to the system size, decay exponentially for Gibbs ensembles and polynomially for generalized Gibbs ensembles, which are in agreement with the finite-size fluctuation within thermodynamic ensembles. Our method paves a path toward studying the thermodynamic and statistical properties of quantum many-body systems in quantum hardware.

quant-ph↗

arXiv2022

Onsager's Scars in Disordered Spin Chains

We propose a class of non-integrable quantum spin chain models that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct such scarred models for arbitrary spin quantum number $ S $. There are two types of scar states, namely, coherent states associated to an Onsager-algebra element and one-magnon scar states. While both of them are highly-excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also investigate the dynamics of the fidelity and entanglement entropy for several initial states. The results clearly show that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly. To our knowledge, our model is the first explicit example of disordered quantum many-body scarred model.

quant-ph↗

arXiv2022

Generalized quantum subspace expansion

One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop practical hardware-friendly quantum error mitigation (QEM) techniques to suppress unwanted errors. Here, we propose a novel generalized quantum subspace expansion method which can handle stochastic, coherent, and algorithmic errors in quantum computers. By fully exploiting the substantially extended subspace, we can efficiently mitigate the noise present in the spectra of a given Hamiltonian, without relying on any information of noise. The performance of our method is discussed under two highly practical setups: the quantum subspaces are mainly spanned by powers of the noisy state $ρ^m$ and a set of error-boosted states, respectively. We numerically demonstrate in both situations that we can suppress errors by orders of magnitude, and show that out protocol inherits the advantages of previous error-agnostic QEM techniques as well as overcoming their drawbacks.

quant-ph↗

arXiv2022

Variational Quantum Simulation for Periodic Materials

We present a quantum-classical hybrid algorithm that simulates electronic structures of periodic systems such as ground states and quasiparticle band structures. By extending the unitary coupled cluster (UCC) theory to describe crystals in arbitrary dimensions, for a hydrogen chain, we numerically demonstrate that the UCC ansatz implemented on a quantum circuit can be successfully optimized with a small deviation from the exact diagonalization over the entire range of the potential energy curves. Furthermore, by using the quantum subspace expansion method, in which we truncate the Hilbert space within the linear response regime from the ground state, the quasiparticle band structure is computed as charged excited states. Our work establishes a powerful interface between the rapidly developing quantum technology and modern material science.

quant-ph↗

arXiv2021

Quantum Fluctuation Theorem under Continuous Measurement and Feedback

While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, an intriguing situation in quantum systems, namely under continuous feedback, remains to be investigated. In this work, we derive the generalized fluctuation theorem under continuous quantum measurement and feedback. The essence for the derivation is to newly introduce the operationally meaningful information, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis. We also verify our theoretical results by numerical simulation and propose an experiment-numerics hybrid verification method. Our work reveals a fundamental connection between quantum thermodynamics and quantum information, which can be experimentally tested with artificial quantum systems such as circuit quantum electrodynamics.

cond-mat.stat-mech↗

arXiv2021

Purifying Deep Boltzmann Machines for Thermal Quantum States

We develop two cutting-edge approaches to construct deep neural networks representing the purified finite-temperature states of quantum many-body systems. Both methods commonly aim to represent the Gibbs state by a highly expressive neural-network wave function, exemplifying the idea of purification. The first method is an entirely deterministic approach to generate deep Boltzmann machines representing the purified Gibbs state exactly. This strongly assures the remarkable flexibility of the ansatz which can fully exploit the quantum-to-classical mapping. The second method employs stochastic sampling to optimize the network parameters such that the imaginary time evolution is well approximated within the expressibility of neural networks. Numerical demonstrations for transverse-field Ising models and Heisenberg models show that our methods are powerful enough to investigate the finite-temperature properties of strongly correlated quantum many-body systems, even when the problematic effect of frustration is present.

cond-mat.str-el↗

arXiv2021

Solving Quasiparticle Band Spectra of Real Solids using Neural-Network Quantum States

Establishing a predictive ab initio method for solid systems is one of the fundamental goals in condensed matter physics and computational materials science. The central challenge is how to encode a highly-complex quantum-many-body wave function compactly. Here, we demonstrate that artificial neural networks, known for their overwhelming expressibility in the context of machine learning, are excellent tool for first-principles calculations of extended periodic materials. We show that the ground-state energies in real solids in one-, two-, and three-dimensional systems are simulated precisely, reaching their chemical accuracy. The highlight of our work is that the quasiparticle band spectra, which are both essential and peculiar to solid-state systems, can be efficiently extracted with a computational technique designed to exploit the low-lying energy structure from neural networks. This work opens up a path to elucidate the intriguing and complex many-body phenomena in solid-state systems.

cond-mat.str-el↗

arXiv2020

Variational Quantum Algorithm for Non-equilibrium Steady States

We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization technique for a unitary quantum circuit, we map a mixed state into a pure state with a doubled number of qubits and design the unitary quantum circuit to fulfill the requirements for a density matrix. This allows us to define a cost function that consists of the time evolution generator of the quantum master equation. Evaluation of physical observables is, in turn, carried out by a quantum circuit with the original number of qubits. We demonstrate our dVQE scheme by both numerical simulation on a classical computer and actual quantum simulation that makes use of the device provided in Rigetti Quantum Cloud Service.

quant-ph↗

arXiv2020

Error bounds for constrained dynamics in gapped quantum systems: Rigorous results and generalizations

In arXiv:2001.03419 we introduce a universal error bound for constrained unitary dynamics within a well-gapped energy band of an isolated quantum system. Here, we provide the full details on the derivation of the bound. In addition, we generalize the result to isolated quantum many-body systems by employing the local Schrieffer-Wolff transformation, obtaining an error bound that grows polynomially in time. We also generalize the result to Markovian open quantum systems and quantitatively explain the quantum Zeno effect.

quant-ph↗

arXiv2020

Universal Error Bound for Constrained Quantum Dynamics

It is well known in quantum mechanics that a large energy gap between a Hilbert subspace of specific interest and the remainder of the spectrum can suppress transitions from the quantum states inside the subspace to those outside due to additional couplings that mix these states, and thus approximately lead to a constrained dynamics within the subspace. While this statement has widely been used to approximate quantum dynamics in various contexts, a general and quantitative justification stays lacking. Here we establish an observable-based error bound for such a constrained-dynamics approximation in generic gapped quantum systems. This universal bound is a linear function of time that only involves the energy gap and coupling strength, provided that the latter is much smaller than the former. We demonstrate that either the intercept or the slope in the bound is asymptotically saturable by simple models. We generalize the result to quantum many-body systems with local interactions, for which the coupling strength diverges in the thermodynamic limit while the error is found to grow no faster than a power law $t^{d+1}$ in $d$ dimensions. Our work establishes a universal and rigorous result concerning nonequilibrium quantum dynamics.

quant-ph↗

arXiv2019

Constructing neural stationary states for open quantum many-body systems

We propose a new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems. Using the high expressive power of the variational ansatz described by the restricted Boltzmann machines, which we dub as the neural stationary state ansatz, we compute the stationary states of quantum dynamics obeying the Lindblad master equations. The mapping of the stationary-state search problem into finding a zero-energy ground state of an appropriate Hermitian operator allows us to apply the conventional variational Monte Carlo method for the optimization. Our method is shown to simulate various spin systems efficiently, i.e., the transverse-field Ising models in both one and two dimensions and the XYZ model in one dimension.

cond-mat.dis-nn↗