arXiv subjects

Naoki Yamamoto

Publications and source records attributed to Naoki Yamamoto.

At least 55 records · Page 3Linked to original sources

arXiv2025

Heisenberg-limited adaptive gradient estimation for multiple observables

In quantum mechanics, measuring the expectation value of a general observable has an inherent statistical uncertainty that is quantified by variance or mean squared error of measurement outcome. While the uncertainty can be reduced by averaging several samples, the number of samples should be minimized when each sample is very costly. This is especially the case for fault-tolerant quantum computing that involves measurement of multiple observables of non-trivial states in large quantum systems that exceed the capabilities of classical computers. In this work, we provide an adaptive quantum algorithm for estimating the expectation values of $M$ general observables within root mean squared error $\varepsilon$ simultaneously, using $\mathcal{O}(\varepsilon^{-1}\sqrt{M}\log M)$ queries to a state preparation oracle of a target state. This remarkably achieves the scaling of Heisenberg limit $1/\varepsilon$, a fundamental bound on the estimation precision in terms of mean squared error, together with the sublinear scaling of the number of observables $M$. The proposed method is an adaptive version of the quantum gradient estimation algorithm and has a resource-efficient implementation due to its adaptiveness. Specifically, the space overhead in the proposed method is $\mathcal{O}(M)$ which is independent from the estimation precision $\varepsilon$ unlike non-iterative algorithms. In addition, our method can avoid the numerical instability problem for constructing quantum circuits in a large-scale task (e.g., $\varepsilon\ll 1$ in our case), which appears in the actual implementation of many algorithms relying on quantum signal processing techniques. Our method paves a new way to precisely understand and predict various physical properties in complicated quantum systems using quantum computers.

quant-ph↗

arXiv2025

Quantum Hall liquids in high-density QCD

There exist metastable domain walls of the flavor-singlet meson $η$ for the ${\rm U}(1)$ axial symmetry in two-flavor color superconductivity (2SC) in QCD at large baryon density. We show that, due to the coupling of $η$ to confined ${\rm SU}(2)$ gluons in the 2SC phase, the effective theory on the domain wall is described by the ${\rm SU}(2)_{-1}$ Chern-Simons theory, which is dual to the ${\rm U}(1)_{2}$ Chern-Simons theory. This theory has a spin-1 droplet excitation that does not carry a baryon number, which we identify as a vector meson. We also discuss the effective theories and baryonic droplet excitations on the domain walls of the flavor-singlet mesons in the superfluid phases of QCD at large isospin density and two-color QCD at large baryon density.

hep-th↗

arXiv2025

Quantum algorithm for partial differential equations of non-conservative systems with spatially varying parameters

Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large computational models is essential for improving product performance and reducing development costs. However, solving large-scale PDEs, particularly for systems with spatially varying material properties, poses significant computational challenges. In this paper, we propose a quantum algorithm for solving second-order linear PDEs of non-conservative systems with spatially varying parameters, using the linear combination of Hamiltonian simulation (LCHS) method. Our approach transforms those PDEs into ordinary differential equations represented by qubit operators, through spatial discretization using the finite difference method. Then, we provide an algorithm that efficiently constructs the operator corresponding to the spatially varying parameters of PDEs via a logic minimization technique, which reduces the number of terms and subsequently the circuit depth. We also develop a scalable method for realizing a quantum circuit for LCHS, using a tensor-network-based technique, specifically a matrix product state (MPS). We validate our method with applications to the acoustic equation with spatially varying parameters and the dissipative heat equation. Our approach includes a detailed recipe for constructing quantum circuits for PDEs, leveraging efficient encoding of spatially varying parameters of PDEs and scalable implementation of LCHS, which we believe marks a significant step towards advancing quantum computing's role in solving practical engineering problems.

quant-ph↗

arXiv2025

Unveiling the nature of cathodoluminescence from photon statistics

Cathodoluminescence (CL), the emission of light induced by accelerated free electrons, has been extensively utilized in various applications, such as displays, streak cameras, and high-spatial-resolution analysis of optical material, surpassing the diffraction limit of light. Despite its long history, the photon statistics of CL have only recently been examined, revealing unexpectedly large bunching of photons. Here we find that this peculiar photon bunching contains information of intervening excitation processes before the photon emission, which can be extracted from the photon statistics within each excitation event by a single free electron. Using this approach, we experimentally unveiled the statistical differences of coherent CL involving a single electromagnetic interaction process and incoherent CL involving multiple excitation processes. The developed formulation is universally applicable for particle generation processes in general to investigate the nature of cascade reactions.

physics.optics↗

arXiv2025

Recursive Quantum Relaxation for Combinatorial Optimization Problems

Quantum optimization methods use a continuous degree-of-freedom of quantum states to heuristically solve combinatorial problems, such as the MAX-CUT problem, which can be attributed to various NP-hard combinatorial problems. This paper shows that some existing quantum optimization methods can be unified into a solver to find the binary solution which is most likely measured from the optimal quantum state. Combining this finding with the concept of quantum random access codes (QRACs) for encoding bits into quantum states on fewer qubits, we propose an efficient recursive quantum relaxation method called recursive quantum random access optimization (RQRAO) for MAX-CUT. Experiments on standard benchmark graphs with several hundred nodes in the MAX-CUT problem, conducted in a fully classical manner using a tensor network technique, show that RQRAO not only outperforms the Goemans-Williamson and recursive QAOA methods, but also is comparable to state-of-the-art classical solvers. The code is available at \url{https://github.com/ToyotaCRDL/rqrao}.

quant-ph↗

arXiv2024

Statistical inference for quantum singular models

Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical statistical models, it is naturally expected that quantum singular models will play a vital role in many quantum statistical tasks. However, while the theory of quantum statistical models in regular cases has been established, theoretical understanding of quantum singular models is still limited. To investigate the statistical properties of quantum singular models, we focus on two prominent tasks in quantum statistical inference: quantum state estimation and model selection. In particular, we base our study on classical singular learning theory and seek to extend it within the framework of Bayesian quantum state estimation. To this end, we define quantum generalization and training loss functions and give their asymptotic expansions through algebraic geometrical methods. The key idea of the proof is the introduction of a quantum analog of the likelihood function using classical shadows. Consequently, we construct an asymptotically unbiased estimator of the quantum generalization loss, the quantum widely applicable information criterion (QWAIC), as a computable model selection metric from given measurement outcomes.

quant-ph↗

arXiv2024

Feedback-driven quantum reservoir computing for time-series analysis

Quantum reservoir computing (QRC) is a highly promising computational paradigm that leverages quantum systems as a computational resource for nonlinear information processing. While its application to time-series analysis is eagerly anticipated, prevailing approaches suffer from the collapse of the quantum state upon measurement, resulting in the erasure of temporal input memories. Neither repeated initializations nor weak measurements offer a fundamental solution, as the former escalates the time complexity while the latter restricts the information extraction from the Hilbert space. To address this issue, we propose the feedback-driven QRC framework. This methodology employs projective measurements on all qubits for unrestricted access to the quantum state, with the measurement outcomes subsequently fed back into the reservoir to restore the memory of prior inputs. We demonstrate that our QRC successfully acquires the fading-memory property through the feedback connections, a critical element in time-series processing. Notably, analysis of measurement trajectories reveal three distinct phases depending on the feedback strength, with the memory performance maximized at the edge of chaos. We also evaluate the predictive capabilities of our QRC, demonstrating its suitability for forecasting signals originating from quantum spin systems.

quant-ph↗

arXiv2024

Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits

Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a potential and promising approach to achieve this purpose. Actually, there are several oracle-based Hamiltonian simulations with potential quantum speedup, but their detailed implementations and accordingly the detailed computational complexities are all unclear. This paper presents a method that enables us to explicitly implement the quantum circuit for Hamiltonian simulation; the key technique is the explicit gate construction of differential operators contained in the target partial differential equation discretized by the finite difference method. Moreover, we show that the space and time complexities of the constructed circuit are exponentially smaller than those of conventional classical algorithms. We also provide numerical experiments and an experiment on a real device for the wave equation to demonstrate the validity of our proposed method.

quant-ph↗

arXiv2024

Quantum-enhanced mean value estimation via adaptive measurement

Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum computing algorithms. Notably, the quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cramér-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. Because the estimation precision directly determines the performance of those quantum technological systems, it is highly demanded to develop a generic and practically implementable estimation method that achieves the QCR bound. Under imperfect conditions, however, such an ultimate and implementable estimator for quantum mean values has not been developed. In this paper, we propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that asymptotically achieves the QCR bound in the limit of a large number of qubits. To approach the QCR bound in a practical setting, the method adaptively optimizes the amplitude amplification and a specific measurement that can be implemented without any knowledge of state preparation. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimator such as consistency and asymptotic normality. Furthermore, several numerical simulations are provided to demonstrate the effectiveness of the method, particularly showing that the estimator needs only a modest number of measurements to almost saturate the QCR bound.

quant-ph↗

arXiv2024

Quantum Inception Score

Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the (classical) inception score (cIS). In this paper, as a natural extension of cIS, we propose the quantum inception score (qIS) for quantum generators. Importantly, qIS relates the quality to the Holevo information of the quantum channel that classifies a given dataset. In this context, we show several properties of qIS. First, qIS is greater than or equal to the corresponding cIS, which is defined through projection measurements on the system output. Second, the difference between qIS and cIS arises from the presence of quantum coherence, as characterized by the resource theory of asymmetry. Third, when a set of entangled generators is prepared, there exists a classifying process leading to the further enhancement of qIS. Fourth, we harness the quantum fluctuation theorem to characterize the physical limitation of qIS. Finally, we apply qIS to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics.

quant-ph↗

arXiv2024

Impact of Measurement Noise on Escaping Saddles in Variational Quantum Algorithms

Stochastic gradient descent (SGD) is a frequently used optimization technique in classical machine learning and Variational Quantum Eigensolver (VQE). For the implementation of VQE on quantum hardware, the results are always affected by measurement shot noise. However, there are many unknowns about the structure and properties of the measurement noise in VQE and how it contributes to the optimization. In this work, we analyze the effect of measurement noise to the optimization dynamics. Especially, we focus on escaping from saddle points in the loss landscape, which is crucial in the minimization of the non-convex loss function. We find that the escape time (1) decreases as the measurement noise increases in a power-law fashion and (2) is expressed as a function of $η/N_s$ where $η$ is the learning rate and $N_s$ is the number of measurements. The latter means that the escape time is approximately constant when we vary $η$ and $N_s$ with the ratio $η/N_s$ held fixed. This scaling behavior is well explained by the stochastic differential equation (SDE) that is obtained by the continuous-time approximation of the discrete-time SGD. According to the SDE, $η/N_s$ is interpreted as the variance of measurement shot noise. This result tells us that we can learn about the optimization dynamics in VQE from the analysis based on the continuous-time SDE, which is theoretically simpler than the original discrete-time SGD.

quant-ph↗

arXiv2024

Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations

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.

quant-ph↗

arXiv2024

Approximate complex amplitude encoding algorithm and its application to data classification problems

Quantum computing has a potential to accelerate the data processing efficiency, especially in machine learning, by exploiting special features such as the quantum interference. The major challenge in this application is that, in general, the task of loading a classical data vector into a quantum state requires an exponential number of quantum gates. The approximate amplitude encoding (AAE) method, which uses a variational means to approximately load a given real-valued data vector into the amplitude of a quantum state, was recently proposed as a general approach to this problem mainly for near-term devices. However, AAE cannot load a complex-valued data vector, which narrows its application range. In this work, we extend AAE so that it can handle a complex-valued data vector. The key idea is to employ the fidelity distance as a cost function for optimizing a parameterized quantum circuit, where the classical shadow technique is used to efficiently estimate the fidelity and its gradient. We apply this algorithm to realize the complex-valued-kernel binary classifier called the compact Hadamard classifier, and then give a numerical experiment showing that it enables classification of Iris dataset and credit card fraud detection.

quant-ph↗

arXiv2024

Accelerating Grover Adaptive Search: Qubit and Gate Count Reduction Strategies with Higher-Order Formulations

Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this paper, we propose higher-order binary formulations that can simultaneously reduce the numbers of qubits and gates required for GAS. Specifically, we consider two novel strategies: one that reduces the number of gates through polynomial factorization, and the other that halves the order of the objective function, subsequently decreasing circuit runtime and implementation cost. Our analysis demonstrates that the proposed higher-order formulations improve the convergence performance of GAS by both reducing the search space size and the number of quantum gates. Our strategies are also beneficial for general combinatorial optimization problems using one-hot encoding.

quant-ph↗

arXiv2024

Entanglement-assisted phase estimation algorithm for calculating dynamical response functions

Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE), where the energy spectra are directly extracted from the QPE measurement outcomes in the frequency domain. Accurate estimation of excitation energies and transition probabilities with these QPE-based approaches is, however, challenging because of the problem of spectral leakage (or peak broadening) which is inherent in the QPE algorithm. To overcome this issue, in this work we consider an extension of the QPE-based approach adopting the optimal entangled input states, which is known to achieve the Heisenberg-limited scaling for the estimation precision. We show that with this method the peaks in the calculated energy spectra are more localized than those calculated by the original QPE-based approaches, suggesting the mitigation of the spectral leakage problem. By analyzing the probability distribution with the entangled phase estimation, we propose a simple scheme to better estimate both the transition energies and the corresponding transition probabilities of the peaks of interest in the spectra. The validity of our prescription is demonstrated by numerical simulations in various quantum many-body problems: the spectral function of a simple electron-plasmon model in condensed-matter physics, the dipole transitions of the H$_2$O molecule in quantum chemistry, and the electromagnetic transitions of the $^6$Li nucleus in nuclear physics.

quant-ph↗

arXiv2024

Quantum conjugate gradient method using the positive-side quantum eigenvalue transformation

Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce the quantum conjugate gradient (QCG) method using the quantum eigenvalue transformation (QET). The circuit depth of this algorithm depends on the square root of the coefficient matrix's condition number $κ$, representing a square root improvement compared to the previous quantum algorithms, while the total query complexity worsens. The number of ancilla qubits is constant, similar to other QET-based algorithms. Additionally, to implement the QCG method efficiently, we devise a QET-based technique that uses only the positive side of the polynomial (denoted by $P(x)$ for $x\in[0,1]$). We conduct numerical experiments by applying our algorithm to the one-dimensional Poisson equation and successfully solve it. Based on the numerical results, our algorithm significantly improves circuit depth, outperforming another QET-based algorithm by three to four orders of magnitude.

quant-ph↗

arXiv2024

Convergence of Ginzburg-Landau expansions: superconductivity in the Bardeen-Cooper-Schrieffer theory and chiral symmetry breaking in the Nambu-Jona-Lasinio model

We study the convergence of the Ginzburg-Landau (GL) expansion in the context of the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity and the Nambu-Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature $T$ and chemical potential $μ$. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap $Δ$ and dynamical quark mass $M$ are given by $Δ_\text{conv} = πT$ and $M_\text{conv} = \sqrt{μ^2 + (πT)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition.

hep-th↗

arXiv2024

Noise Robustness of Quantum Relaxation for Combinatorial Optimization

QRAO (Quantum Random Access Optimization) is a relaxation algorithm that reduces the number of qubits required to solve a problem by encoding multiple variables per qubit using QRAC (Quantum Random Access Code). Reducing the number of qubits is a common way of dealing with the impact of noise on a quantum algorithm. Our interest lies in the impact of noise on the quality of the binary solution of QRAO, which is unknown. We demonstrate that the mean approximation ratio of the (3, 1)-QRAC Hamiltonian, i.e., the Hamiltonian utilizing the encoding of 3 bits into 1 qubit by QRAC, is less affected by noise compared to the Ising Hamiltonian used in quantum annealer and QAOA (Quantum Approximate Optimization Algorithm). Based on this observation, we discuss a plausible mechanism behind the robustness of QRAO under depolarizing noise. Finally, we assess the number of shots required to estimate the values of binary variables correctly under depolarizing noise and show that the (3, 1)-QRAC Hamiltonian requires less shots to achieve the same accuracy compared to the Ising Hamiltonian.

quant-ph↗