arXiv subjects

Yuki Sato

Publications and source records attributed to Yuki Sato.

At least 55 records · Page 3Linked to original sources

arXiv2024

Deep-learning-based Magnetic Resonance Simultaneous Multislice Imaging Using Holographic Image Decoding

Simultaneous multislice (SMS) imaging is a one of the acceleration technique of magnetic resonance imaging. SMS requires accurate sensitivity distributions in the slice plane for each receiving coil. This requirement is difficult to satisfy in practice, limiting the applications of this imaging technique. Here, images are reconstructed by applying deep learning and amplitude modulation to each slice image. Simulation experiments show that image reconstruction can be achieved for both real- and complex-valued images. Image quality tends to decrease with increasing number of simultaneously acquired images. It is also shown that a larger difference in the phase modulation coefficients between slices tends to increase the quality of the reconstructed images. Simulation experiments and initial MR imaging experiments show promising results for this method.

physics.med-ph↗

arXiv2023

Exact solution to a generalised Lillo-Mike-Farmer model with heterogeneous order-splitting strategies

The Lillo-Mike-Farmer (LMF) model is an established econophysics model describing the order-splitting behaviour of institutional investors in financial markets. In the original article (LMF, Physical Review E 71, 066122 (2005)), LMF assumed the homogeneity of the traders' order-splitting strategy and derived a power-law asymptotic solution to the order-sign autocorrelation function (ACF) based on several heuristic reasonings. This report proposes a generalised LMF model by incorporating the heterogeneity of traders' order-splitting behaviour that is exactly solved without heuristics. We find that the power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous intensity distributions. On the other hand, the prefactor in the ACF is very sensitive to heterogeneity in trading strategies and is shown to be systematically underestimated in the original homogeneous LMF model. Our work highlights that the ACF prefactor should be more carefully interpreted than the ACF power-law exponent in data analyses.

q-fin.TR↗

arXiv2023

Variational quantum algorithm for generalized eigenvalue problems and its application to the finite element method

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the key problems to handle GEPs is that the memory usage and computational complexity explode as the size of the system of interest grows. This paper aims at extending sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms that iteratively solve the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the GEP as the minimization/maximization problem of the fractional form of the expectations of two Hermitians. We then showed that the fractional objective function can be analytically minimized or maximized with respect to a single-qubit gate by solving a GEP of a 4 $\times$ 4 matrix. Second, we show that a system of linear equations (SLE) characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to important engineering problems formulated with the finite element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method.

quant-ph↗

arXiv2023

Quantum channel decomposition with pre- and post-selection

The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate/wire cutting, are powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently executing relatively easy-to-implement (or noisy) quantum channels. However, such virtual simulation necessitates an exponentially large number of decompositions, thereby significantly limiting their practical applicability. This paper proposes a channel decomposition method for target unitaries that have their input and output conditioned on specific quantum states, namely unitaries with pre- and post-selection. Specifically, we explicitly determine the requisite number of decomposing channels, which could be significantly smaller than the selection-free scenario. Furthermore, we elucidate the structure of the resulting decomposed unitary. We demonstrate an application of this approach to the quantum linear solver algorithm, highlighting the efficacy of the proposed method.

quant-ph↗

arXiv2023

Can we infer microscopic financial information from the long memory in market-order flow?: a quantitative test of the Lillo-Mike-Farmer model

In financial markets, the market order sign exhibits strong persistence, widely known as the long-range correlation (LRC) of order flow; specifically, the sign correlation function displays long memory with power-law exponent $γ$, such that $C(τ) \propto τ^{-γ}$ for large time-lag $τ$. One of the most promising microscopic hypotheses is the order-splitting behaviour at the level of individual traders. Indeed, Lillo, Mike, and Farmer (LMF) introduced in 2005 a simple microscopic model of order-splitting behaviour, which predicts that the macroscopic sign correlation is quantitatively associated with the microscopic distribution of metaorders. While this hypothesis has been a central issue of debate in econophysics, its direct quantitative validation has been missing because it requires large microscopic datasets with high resolution to observe the order-splitting behaviour of all individual traders. Here we present the first quantitative validation of this LFM prediction by analysing a large microscopic dataset in the Tokyo Stock Exchange market for more than nine years. On classifying all traders as either order-splitting traders or random traders as a statistical clustering, we directly measured the metaorder-length distributions $P(L)\propto L^{-α-1}$ as the microscopic parameter of the LMF model and examined the theoretical prediction on the macroscopic order correlation: $γ\approx α- 1$. We discover that the LMF prediction agrees with the actual data even at the quantitative level. Our work provides the first solid support of the microscopic model and solves directly a long-standing problem in the field of econophysics and market microstructure.

q-fin.TR↗

arXiv2023

Quantitative statistical analysis of order-splitting behaviour of individual trading accounts in the Japanese stock market over nine years

In this research, we focus on the order-splitting behavior. The order splitting is a trading strategy to execute their large potential metaorder into small pieces to reduce transaction cost. This strategic behavior is believed to be important because it is a promising candidate for the microscopic origin of the long-range correlation (LRC) in the persistent order flow. Indeed, in 2005, Lillo, Mike, and Farmer (LMF) introduced a microscopic model of the order-splitting traders to predict the asymptotic behavior of the LRC from the microscopic dynamics, even quantitatively. The plausibility of this scenario has been qualitatively investigated by Toth et al. 2015. However, no solid support has been presented yet on the quantitative prediction by the LMF model in the lack of large microscopic datasets. In this report, we have provided the first quantitative statistical analysis of the order-splitting behavior at the level of each trading account. We analyse a large dataset of the Tokyo stock exchange (TSE) market over nine years, including the account data of traders (called virtual servers). The virtual server is a unit of trading accounts in the TSE market, and we can effectively define the trader IDs by an appropriate preprocessing. We apply a strategy clustering to individual traders to identify the order-splitting traders and the random traders. For most of the stocks, we find that the metaorder length distribution obeys power laws with exponent $α$, such that $P(L)\propto L^{-α-1}$ with the metaorder length $L$. By analysing the sign correlation $C(τ)\propto τ^{-γ}$, we directly confirmed the LMF prediction $γ\approx α-1$. Furthermore, we discuss how to estimate the total number of the splitting traders only from public data via the ACF prefactor formula in the LMF model. Our work provides the first quantitative evidence of the LMF model.

q-fin.TR↗

arXiv2023

4D topology optimization: Integrated optimization of the structure and self-actuation of soft bodies for dynamic motions

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited deformations and contact capabilities. Designing soft and actively moving objects, such as soft robots equipped with actuators, poses challenges due to simulating dynamics problems involving large deformations and intricate contact interactions. Moreover, the optimal structure depends on the object's motion, necessitating a simultaneous design approach. To address these challenges, we propose "4D topology optimization," an extension of density-based topology optimization that incorporates the time dimension. This enables the simultaneous optimization of both the structure and self-actuation of soft bodies for specific dynamic tasks. Our method utilizes multi-indexed and hierarchized density variables distributed over the spatiotemporal design domain, representing the material layout, actuator layout, and time-varying actuation. These variables are efficiently optimized using gradient-based methods. Forward and backward simulations of soft bodies are done using the material point method, a Lagrangian-Eulerian hybrid approach, implemented on a recent automatic differentiation framework. We present several numerical examples of self-actuating soft body designs aimed at achieving locomotion, posture control, and rotation tasks. The results demonstrate the effectiveness of our method in successfully designing soft bodies with complex structures and biomimetic movements, benefiting from its high degree of design freedom.

cs.CE↗

arXiv2023

Quantum critical dynamics in a 5000-qubit programmable spin glass

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Due to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization. Here we achieve this goal by realizing quantum critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and time-evolution of the Schrödinger equation in small spin glasses. We then measure dynamics in 3D spin glasses on thousands of qubits, where simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for a scaling advantage in reducing energy as a function of annealing time.

quant-ph↗

arXiv2023

Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver

Variational Quantum Eigensolver (VQE) is a hybrid algorithm for finding the minimum eigenvalue/vector of a given Hamiltonian by optimizing a parametrized quantum circuit (PQC) using a classical computer. Sequential optimization methods, which are often used in quantum circuit tensor networks, are popular for optimizing the parametrized gates of PQCs. This paper focuses on the case where the components to be optimized are single-qubit gates, in which the analytic optimization of a single-qubit gate is sequentially performed. The analytical solution is given by diagonalization of a matrix whose elements are computed from the expectation values of observables specified by a set of predetermined parameters which we call the parameter configurations. In this study, we first show that the optimization accuracy significantly depends on the choice of parameter configurations due to the statistical errors in the expectation values. We then identify a metric that quantifies the optimization accuracy of a parameter configuration for all possible statistical errors, named configuration overhead/cost or C-cost. We theoretically provide the lower bound of C-cost and show that, for the minimum size of parameter configurations, the lower bound is achieved if and only if the parameter configuration satisfies the so-called equiangular line condition. Finally, we provide numerical experiments demonstrating that the optimal parameter configuration exhibits the best result in several VQE problems. We hope that this general statistical methodology will enhance the efficacy of sequential optimization of PQCs for solving practical problems with near-term quantum devices.

quant-ph↗

arXiv2023

Topology optimization of locomoting soft bodies using material point method

Topology optimization methods have widely been used in various industries, owing to their potential for providing promising design candidates for mechanical devices. However, their applications are usually limited to the objects which do not move significantly due to the difficulty in computationally efficient handling of the contact and interactions among multiple structures or with boundaries by conventionally used simulation techniques. In the present study, we propose a topology optimization method for moving objects incorporating the material point method, which is often used to simulate the motion of objects in the field of computer graphics. Several numerical experiments demonstrate the effectiveness and the utility of the proposed method.

cs.CE↗

arXiv2023

Sequential optimal selection of a single-qubit gate and its relation to barren plateau in parameterized quantum circuits

We propose an algorithm for variational quantum algorithms (VQAs) to optimize the structure of parameterized quantum circuits (PQCs) efficiently. The algorithm optimizes the PQC structure on-the-fly in VQA by sequentially replacing a single-qubit gate with the optimal one to minimize the objective function. To directly find the optimal gate, our method uses the factorization of matrices whose elements are evaluated on a set of the slightly-modified circuits. The matrix factorization enables us to not only unify the existing sequential methods for further extension but also provide rigorous proofs of their limitation and potential in comparison with conventional gradient-based optimizers. Firstly, when the circuits are sufficiently deep, the sequential methods encounter a barren plateau that the spectrum of the matrix concentrates on a single value exponentially fast with respect to the number of qubits. Secondly, if the objective functions are local observables, they can avoid barren plateaus as long as the depth of the n-qubit PQCs is $O(\log{n})$. Although the family of these optimizers does not directly employ gradients of the objective function, our results establish their connection with conventional optimizations providing a consistent picture of the barren plateau. We also perform numerical experiments showing the advantages over conventional VQAs and confirm the successful optimization getting over the barren plateau in the ground state problem of the mixed field Ising model up to 12 qubits.

quant-ph↗

arXiv2022

Tensor network approach to 2d Lorentzian quantum Regge calculus

We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices. The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average edge length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries, although the investigation of the higher moments is required to make the statement more conclusive. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity.

hep-th↗

arXiv2022

Free material optimization of thermal conductivity tensors with asymmetric components

Free Material Optimization (FMO), a branch of topology optimization, in which the design variables are the full constitutive tensors, can provide the most general form of the design problems. Considering the microstructure composed of isotropic materials, the constitutive tensors are yet positive definite and symmetric. On the other hand, it has been reported that the symmetry of this constitutive tensor can be broken in appearance by considering other physical phenomena. In the present study, we focus on the thermal Hall effect, which is explained as the phenomena that induces the temperature gradient orthogonal to a given temperature gradient across a solid when a magnetic field is applied to the solid. This effect makes the thermal conductivity tensor asymmetric and justifies extending the space of the constitutive tensors to be an asymmetric domain. We propose the FMO for asymmetric constitutive tensors, parameterizing the design space so that the physically available property could be naturally satisfied. Several numerical experiments are provided to show the validity and the utility of the proposed method.

cs.CE↗

arXiv2022

Quantum topology optimization of ground structures using noisy intermediate-scale quantum devices

To arrive at some viable product design, product development processes frequently use numerical simulations and mathematical programming techniques. Topology optimization, in particular, is one of the most promising techniques for generating insightful design choices. Topology optimization problems reduce to an NP-hard combinatorial optimization problem, where the combination of the existence or absence of the material at some positions is optimized. In this study, we examine the usage of quantum computers as a potential solution to topology optimization problems. The proposed method consists of two variational quantum algorithms (VQAs): the first solves the state equilibrium equation for all conceivable material configurations, while the second amplifies the likelihood of an optimal configuration in quantum superposition using the first VQA's quantum state. Several experiments, including a real device experiment, show that the proposed method successfully obtained the optimal configurations. These findings suggest that quantum computers could be a potential tool for solving topology optimization problems and they open the window to the near-future product designs.

quant-ph↗

arXiv2022

Resistivity and Thermal Conductivity of an Organic Insulator beta'-EtMe3Sb[Pd(dmit)2]2

A finite residual linear term in the thermal conductivity at zero temperature in insulating magnets indicates the presence of gapless excitations of itinerant quasiparticles, which has been observed in some candidate materials of quantum spin liquids (QSLs). In the organic triangular insulator beta'-EtMe3Sb[Pd(dmit)2]2, a QSL candidate material, the low-temperature thermal conductivity depends on the cooling process and the finite residual term is observed only in samples with large thermal conductivity. Moreover, the cooling rate dependence is largely sample dependent. Here we find that, while the low-temperature thermal conductivity significantly depends on the cooling rate, the high-temperature resistivity is almost perfectly independent of the cooling rate. These results indicate that in the samples with the finite residual term, the mean free path of the quasiparticles that carry the heat at low temperatures is governed by disorders, whose characteristic length scale of the distribution is much longer than the electron mean free path that determines the high-temperature resistivity. This explains why recent X-ray diffraction and nuclear magnetic resonance measurements show no cooling rate dependence. Naturally, these measurements are unsuitable for detecting disorders of the length scale relevant for the thermal conductivity, just as they cannot determine the residual resistivity of metals. Present results indicate that very careful experiments are needed when discussing itinerant spin excitations in beta'-EtMe3Sb[Pd(dmit)2]2.

cond-mat.str-el↗

arXiv2022

Hall anomaly, Quantum Oscillations and Possible Lifshitz Transitions in Kondo Insulator YbB$_{12}$: Evidence for Unconventional Charge Transport

In correlated electronic systems, strong interactions and the interplay between different degrees of freedom may give rise to anomalous charge transport properties, which can be tuned by external parameters like temperature and magnetic field. Recently, magnetic quantum oscillations and metallic low-temperature thermal conductivity have been observed in the Kondo insulator YbB$_{12}$, whose resistivity is a few orders of magnitude higher than those of conventional metals. As yet, these unusual observations are not fully understood. Here we present a detailed investigation of the behavior of YbB$_{12}$ under intense magnetic fields using both transport and torque magnetometry measurements. A low-field Hall anomaly, reminiscent of the Hall response associated with "strange-metal" physics, develops at $T < 1.5$ K. At two characteristic magnetic fields ($μ_0H_1= 19.6$ T and $μ_0H_2 \sim 31$ T), signatures appear in the Hall coefficient, magnetic torque, and magnetoresistance. We suggest that they are likely to be field-induced Lifshitz transitions. Moreover, above 35 T, the background resistivity displays an unusual, nonmetallic $T^α$-behavior, with $α$ being field-dependent and varying between -1.5 and -2. By normalizing the Shubnikov-de Haas oscillation amplitude to this $T^α$-dependence, the calculated cyclotron mass becomes more consistent with that deduced from de Haas-van Alphen oscillations. Our results support a novel two-fluid scenario in YbB$_{12}$: a Fermi-liquid-like fluid of charge-neutral quasiparticles coexists with charge carriers that remain in a nonmetallic state. The former experience successive Lifshitz transitions and develop Landau quantization in applied magnetic fields, whilst scattering between both fluids allows the Shubnikov-de Haas effect to be observed in the electrical transport.

cond-mat.str-el↗

arXiv2022

Variational quantum algorithm based on the minimum potential energy for solving the Poisson equation

Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often intractable within a reasonable computation time, even when using supercomputers. To overcome the inherent limit of classical computing, we present a variational quantum algorithm for solving the Poisson equation that can be implemented in noisy intermediate-scale quantum devices. The proposed method defines the total potential energy of the Poisson equation as a Hamiltonian, which is decomposed into a linear combination of Pauli operators and simple observables. The expectation value of the Hamiltonian is then minimized with respect to a parameterized quantum state. Because the number of decomposed terms is independent of the size of the problem, this method requires relatively few quantum measurements. Numerical experiments demonstrate the faster computing speed of this method compared with classical computing methods and a previous variational quantum approach. We believe that our approach brings quantum computer-aided techniques closer to future applications in engineering developments. Code is available at https://github.com/ToyotaCRDL/VQAPoisson.

quant-ph↗

arXiv2022

Computationally Efficient Quantum Expectation with Extended Bell Measurements

Evaluating an expectation value of an arbitrary observable $A\in{\mathbb C}^{2^n\times 2^n}$ through naïve Pauli measurements requires a large number of terms to be evaluated. We approach this issue using a method based on Bell measurement, which we refer to as the extended Bell measurement method. This analytical method quickly assembles the $4^n$ matrix elements into at most $2^{n+1}$ groups for simultaneous measurements in $O(nd)$ time, where $d$ is the number of non-zero elements of $A$. The number of groups is particularly small when $A$ is a band matrix. When the bandwidth of $A$ is $k=O(n^c)$, the number of groups for simultaneous measurement reduces to $O(n^{c+1})$. In addition, when non-zero elements densely fill the band, the variance is $O((n^{c+1}/2^n)\,{\rm tr}(A^2))$, which is small compared with the variances of existing methods. The proposed method requires a few additional gates for each measurement, namely one Hadamard gate, one phase gate and at most $n-1$ CNOT gates. Experimental results on an IBM-Q system show the computational efficiency and scalability of the proposed scheme, compared with existing state-of-the-art approaches. Code is available at https://github.com/ToyotaCRDL/extended-bell-measurements.

quant-ph↗