arXiv subjects

Keisuke Fujii

Publications and source records attributed to Keisuke Fujii.

At least 181 records · Page 10Linked to original sources

arXiv2022

Quantum-inspired algorithm applied to extreme learning

Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible through the efficient sampling of matrix elements according to their norms. Here, we apply it to extreme learning which is a machine learning framework that performs linear regression using random feature vectors generated through a random neural network. The extreme learning is suited for the application of quantum-inspired SVD in that it first requires transforming each data to a random feature during which we can construct the data structure with a logarithmic overhead with respect to the number of data. We implement the algorithm and observe that it works order-of-magnitude faster than the exact SVD when we use high-dimensional feature vectors. However, we also observe that, for random features generated by random neural networks, we can replace the norm-based sampling in the quantum-inspired algorithm with uniform sampling to obtain the same level of test accuracy due to the uniformity of the matrix in this case. The norm-based sampling becomes effective for more non-uniform matrices obtained by optimizing the feature mapping. It implies the non-uniformity of matrix elements is a key property of the quantum-inspired SVD. This work is a first step toward the practical application of the quantum-inspired algorithm.

quant-ph↗

arXiv2022

A Practical and Scalable Decoder for Topological Quantum Error Correction with Digital Annealer

Quantum error correction is one of the most important milestones for realization of large-scale quantum computation. To achieve this, it is essential not only to integrate a large number of qubits with high fidelity, but also to build a scalable classical system that can perform error correction. Here, we propose an efficient and scalable decoder for quantum error correction using Fujitsu Digital Annealer (DA). Specifically, the error correction problem of stabilizer codes is mapped into an Ising-type optimization problem, so-called quadratic unconstrained binary optimization (QUBO) problem, which is solved by DA. In particular, we implement the proposed DA decoder for the surface code and perform detailed numerical experiments for various code distances to see its performance and scalability. We observe that computational scaling for the DA decoder has a lower order of polynomial than the decoding methods using simulated annealing (SA) and minimum-weight perfect matching (MWPM) algorithm under all tested conditions. It is also shown that the DA decoder has advantages over the Union-Find (UF) decoder from a variety of perspectives including hardware implementation. Furthermore, the threshold behavior of the logical error probability for the DA decoder is analyzed and the resultant threshold lies between 9.4% and 9.8%, which is very close to that obtained by the MWPM decoder. This result clearly shows the high potential of the DA decoder for quantum error correction.

quant-ph↗

arXiv2022

Automatic detection of faults in race walking from a smartphone camera: a comparison of an Olympic medalist and university athletes

Automatic fault detection is a major challenge in many sports. In race walking, referees visually judge faults according to the rules. Hence, ensuring objectivity and fairness while judging is important. To address this issue, some studies have attempted to use sensors and machine learning to automatically detect faults. However, there are problems associated with sensor attachments and equipment such as a high-speed camera, which conflict with the visual judgement of referees, and the interpretability of the fault detection models. In this study, we proposed a fault detection system for non-contact measurement. We used pose estimation and machine learning models trained based on the judgements of multiple qualified referees to realize fair fault judgement. We verified them using smartphone videos of normal race walking and walking with intentional faults in several athletes including the medalist of the Tokyo Olympics. The validation results show that the proposed system detected faults with an average accuracy of over 90%. We also revealed that the machine learning model detects faults according to the rules of race walking. In addition, the intentional faulty walking movement of the medalist was different from that of university walkers. This finding informs realization of a more general fault detection model. The code and data are available at https://github.com/SZucchini/racewalk-aijudge.

cs.CV↗

arXiv2022

Pitching strategy evaluation via stratified analysis using propensity score

Recent measurement technologies enable us to analyze baseball at higher levels. There are, however, still many unclear points around the pitching strategy. The two elements make it difficult to measure the effect of pitching strategy. First, most public datasets do not include location data where the catcher demands a ball, which is essential information to obtain the battery's intent. Second, there are many confounders associated with pitching/batting results when evaluating pitching strategy. We here clarify the effect of pitching attempts to a specific location, e.g., inside or outside. We employ a causal inference framework called stratified analysis using a propensity score to evaluate the effects while removing the effect of disturbing factors. We used a pitch-by-pitch dataset of Japanese professional baseball games held in 2014-2019, which includes location data where the catcher demands a ball. The results reveal that an outside pitching attempt is more effective than an inside one to minimize allowed run on average. Besides, the stratified analysis shows that the outside pitching attempt was always effective despite the magnitude of the estimated batter's ability, and the ratio of pitched inside for pitcher/batter. Our analysis would provide practical insights into selecting a pitching strategy to minimize allowed runs.

stat.AP↗

arXiv2022

Evaluation of creating scoring opportunities for teammates in soccer via trajectory prediction

Evaluating the individual movements for teammates in soccer players is crucial for assessing teamwork, scouting, and fan engagement. It has been said that players in a 90-min game do not have the ball for about 87 minutes on average. However, it has remained difficult to evaluate an attacking player without receiving the ball, and to reveal how movement contributes to the creation of scoring opportunities for teammates. In this paper, we evaluate players who create off-ball scoring opportunities by comparing actual movements with the reference movements generated via trajectory prediction. First, we predict the trajectories of players using a graph variational recurrent neural network that can accurately model the relationship between players and predict the long-term trajectory. Next, based on the difference in the modified off-ball evaluation index between the actual and the predicted trajectory as a reference, we evaluate how the actual movement contributes to scoring opportunity compared to the predicted movement. For verification, we examined the relationship with the annual salary, the goals, and the rating in the game by experts for all games of a team in a professional soccer league in a year. The results show that the annual salary and the proposed indicator correlated significantly, which could not be explained by the existing indicators and goals. Our results suggest the effectiveness of the proposed method as an indicator for a player without the ball to create a scoring chance for teammates.

cs.AI↗

arXiv2022

Pricing multi-asset derivatives by variational quantum algorithms

Pricing a multi-asset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of derivatives, the computational complexity increases exponentially as the number of underlying assets increases in some classical methods, such as the finite difference method. Therefore, there are efforts to reduce the computational complexity by using quantum computation. However, when solving with naive quantum algorithms, the target derivative price is embedded in the amplitude of one basis of the quantum state, and so an exponential complexity is required to obtain the solution. To avoid the bottleneck, the previous study~[Miyamoto and Kubo, IEEE Transactions on Quantum Engineering, \textbf{3}, 1--25 (2022)] utilizes the fact that the present price of a derivative can be obtained by its discounted expected value at any future point in time and shows that the quantum algorithm can reduce the complexity. In this paper, to make the algorithm feasible to run on a small quantum computer, we use variational quantum simulation to solve the Black-Scholes equation and compute the derivative price from the inner product between the solution and a probability distribution. This avoids the measurement bottleneck of the naive approach and would provide quantum speedup even in noisy quantum computers. We also conduct numerical experiments to validate our method. Our method will be an important breakthrough in derivative pricing using small-scale quantum computers.

quant-ph↗

arXiv2022

Fast Classical Simulation of Hamiltonian Dynamics by Simultaneous Diagonalization Using Clifford Transformation with Parallel Computation

Simulating quantum many-body dynamics is important both for fundamental understanding of physics and practical applications for quantum information processing. Therefore, classical simulation methods have been developed so far. Specifically, the Trotter-Suzuki decomposition can analyze a highly complex quantum dynamics, if the number of qubits is sufficiently small so that main memory can store the state vector. However, simulation of quantum dynamics via Trotter-Suzuki decomposition requires huge number of steps, each of which accesses the state vector, and hence the simulation time becomes impractically long. To settle this issue, we propose a technique to accelerate simulation of quantum dynamics via simultaneous diagonalization of mutually commuting Pauli groups, which is also attracting a lot of attention to reduce the measurement overheads in quantum algorithms. We group the Hamiltonian into mutually commputing Pauli strings, and each of them are diagonalized in the computational basis via a Clifford transformation. Since diagonal operators are applied on the state vector simultaneously with minimum memory access, this method successfully use performance of highly parallel processors such as Graphics Processing Units (GPU). Compared to an implementation using one of the fastest simulators of quantum computers, the numerical experiments have shown that our method provides a few tens of times acceleration.

quant-ph↗

arXiv2022

Estimating the Effect of Team Hitting Strategies Using Counterfactual Virtual Simulation in Baseball

In baseball, every play on the field is quantitatively evaluated and has an effect on individual and team strategies. The weighted on base average (wOBA) is well known as a measure of an batter's hitting contribution. However, this measure ignores the game situation, such as the runners on base, which coaches and batters are known to consider when employing multiple hitting strategies, yet, the effectiveness of these strategies is unknown. This is probably because (1) we cannot obtain the batter's strategy and (2) it is difficult to estimate the effect of the strategies. Here, we propose a new method for estimating the effect using counterfactual batting simulation. To this end, we propose a deep learning model that transforms batting ability when batting strategy is changed. This method can estimate the effects of various strategies, which has been traditionally difficult with actual game data. We found that, when the switching cost of batting strategies can be ignored, the use of different strategies increased runs. When the switching cost is considered, the conditions for increasing runs were limited. Our validation results suggest that our simulation could clarify the effect of using multiple batting strategies.

cs.AI↗

arXiv2022

Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers

Variational quantum eigensolver (VQE), which attracts attention as a promising application of noisy intermediate-scale quantum devices, finds a ground state of a given Hamiltonian by variationally optimizing the parameters of quantum circuits called ansatz. Since the difficulty of the optimization depends on the complexity of the problem Hamiltonian and the structure of the ansatz, it has been difficult to analyze the performance of optimizers for the VQE systematically. To resolve this problem, we propose a technique to construct a benchmark problem whose ground state is guaranteed to be achievable with a given ansatz by using the idea of parent Hamiltonian of low-depth parameterized quantum circuits. We compare the convergence of several optimizers by varying the distance of the initial parameters from the solution and find that the converged energies showed a threshold-like behavior depending on the distance. This work provides a systematic way to analyze optimizers for VQE and contribute to the design of ansatz and its initial parameters.

quant-ph↗

arXiv2022

Evaluation of soccer team defense based on prediction models of ball recovery and being attacked: A pilot study

With the development of measurement technology, data on the movements of actual games in various sports can be obtained and used for planning and evaluating the tactics and strategy. Defense in team sports is generally difficult to be evaluated because of the lack of statistical data. Conventional evaluation methods based on predictions of scores are considered unreliable because they predict rare events throughout the game. Besides, it is difficult to evaluate various plays leading up to a score. In this study, we propose a method to evaluate team defense from a comprehensive perspective related to team performance by predicting ball recovery and being attacked, which occur more frequently than goals, using player actions and positional data of all players and the ball. Using data from 45 soccer matches, we examined the relationship between the proposed index and team performance in actual matches and throughout a season. Results show that the proposed classifiers predicted the true events (mean F1 score $>$ 0.483) better than the existing classifiers which were based on rare events or goals (mean F1 score $<$ 0.201). Also, the proposed index had a moderate correlation with the long-term outcomes of the season ($r =$ 0.397). These results suggest that the proposed index might be a more reliable indicator rather than winning or losing with the inclusion of accidental factors.

cs.AI↗

arXiv2022

Local variational quantum compilation of a large-scale Hamiltonian dynamics

Implementing time evolution operators on quantum circuits is important for quantum simulation. However, the standard way, Trotterization, requires a huge numbers of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows to accurately and efficiently compile a time evolution operators on a large-scale quantum system by the optimization with smaller-size quantum systems. LVQC utilizes a subsystem cost function, which approximates the fidelity of the whole circuit, defined for each subsystem as large as approximate causal cones brought by the Lieb-Robinson (LR) bound. We rigorously derive its scaling property with respect to the subsystem size, and show that the optimization conducted on the subsystem size leads to the compilation of whole-system time evolution operators. As a result, LVQC runs with limited-size quantum computers or classical simulators that can handle such smaller quantum systems. For instance, finite-ranged and short-ranged interacting $L$-size systems can be compiled with $O(L^0)$- or $O(\log L)$-size quantum systems depending on observables of interest. Furthermore, since this formalism relies only on the LR bound, it can efficiently construct time evolution operators of various systems in generic dimension involving finite-, short-, and long-ranged interactions. We also numerically demonstrate the LVQC algorithm for one-dimensional systems. Employing classical simulation by time-evolving block decimation, we succeed in compressing the depth of a time evolution operators up to $40$ qubits by the compilation for $20$ qubits. LVQC not only provides classical protocols for designing large-scale quantum circuits, but also will shed light on applications of intermediate-scale quantum devices in implementing algorithms in larger-scale quantum devices.

quant-ph↗

arXiv2022

A Simple Data-Driven Level Finding Method of Quantum Many-Body Systems based on Statistical Outlier Detection

We report a simple and pure data-driven method to find new energy levels of quantum many-body systems only from observed line wavelengths. In our method, all the possible combinations are computed from known energy levels and wavelengths of unidentified lines. As each excited state exhibits many transition lines to different lower levels, the true levels should be reconstructed coincidentally from many level-line combinations, while the wrong combinations distribute randomly. Such a coincidence can be easily detected statistically. We demonstrate this statistical method by finding new levels for various atomic and nuclear systems from unidentified line lists available online.

physics.atom-ph↗

arXiv2022

Probing heavy Majorana neutrino pair production at ILC in a $U(1)_{\rm B-L}$ extension of the Standard Model

We consider a gauged B$-$L (Baryon number minus Lepton number) extension of the Standard Model (SM), which is anomaly free in the presence of three SM singlet Right Handed Neutrinos (RHNs). Associated with the $U(1)_{\rm B-L}$ gauge symmetry breaking, the RHNs acquire Majorana masses and then with the electroweak symmetry breaking, tiny Majorana masses for the SM(-like) neutrinos are naturally generated by the seesaw mechanism. As a result of the seesaw mechanism, the heavy mass eigenstates which are mainly composed of the SM-singlet RHNs obtain suppressed electroweak interactions through small mixings with the SM neutrinos. To investigate the seesaw mechanism, we study the pair production of heavy Majorana neutrinos through the $U(1)_{\rm B-L}$ gauge boson $Z^\prime$ at the 250 GeV and 500 GeV International Linear Collider (ILC). Considering the current and prospective future bounds on the B$-$L model parameters from the search for a resonant $Z^\prime$ boson production at the Large Hadron Collider (LHC), we focus on a "smoking-gun" signature of the Majorana nature of the heavy neutrinos: a final state with a pair of same-sign, same-flavor leptons, small missing momentum, and four hadronic jets. We estimate the projected significance of the signature at the ILC.

hep-ex↗

arXiv2022

Measurement of $A_{LR}$ using radiative return at ILC 250

For the precision study at the ILC 250, measurement of $A_{LR}$ is important as it can constrain SMEFT parameters. The current best measured $A_{LR}$ value is $A_{LR} = 0.1514 \pm 0.0019\,(stat) \pm 0.0011\,(syst)$ which was measured at the SLC, and a more precise value is required for the global fit for the new physics search in TeV-scale. At the ILC, we can use the $e^+ e^- \to γZ$ process to evaluate the $A_{LR}$. We performed a full simulation study of the $e^+ e^- \to γZ$ process at the center-of-mass energy of 250 GeV and evaluated how much we can improve the precision of this observable. The statistical error on $A_{LR}$ at the ILC 250 turned out to be $1.8 \times 10^{-4}$. Major source of the systematic error was error from the beam polarization. As other sources of the systematic error, the uncorrelated parts of error on the product of luminosity and selection efficiency for each polarization combination contribute. Including those systematic errors, total absolute error on $A_{LR}$ was estimated to be 0.00025, 8.8 times better precision than that from the SLC (0.00219).

hep-ex↗

arXiv2022

Effective field theory of fluctuating wall in open systems: from a kink in Josephson junction to general domain wall

We investigate macroscopic behaviors of fluctuating domain walls in nonequilibrium open systems with the help of the effective field theory based on symmetry. Since the domain wall in open systems breaks the translational symmetry, there appears a gapless excitation identified as the Nambu-Goldstone (NG) mode, which shows the non-propagating diffusive behavior in contrast to those in closed systems. After demonstrating the presence of the diffusive NG mode in the $(2+1)$-dimensional dissipative Josephson junction, we provide a symmetry-based general analysis for open systems breaking the one-dimensional translational symmetry. A general effective Lagrangian is constructed based on the Schwinger-Keldysh formalism, which supports the presence of the gapless diffusion mode in the fluctuation spectrum in the thin wall regime. Besides, we also identify a term peculiar to the open system, which possibly leads to the instability in the thick-wall regime or the nonlinear Kardar-Parisi-Zhang coupling in the thin-wall regime although it is absent in the Josephson junction.

hep-th↗

arXiv2022

Identification of topological phases using classically-optimized variational quantum eigensolver

Variational quantum eigensolver (VQE) is regarded as a promising candidate of hybrid quantum-classical algorithm for the near-term quantum computers. Meanwhile, VQE is confronted with a challenge that statistical error associated with the measurement as well as systematic error could significantly hamper the optimization. To circumvent this issue, we propose classically-optimized VQE (co-VQE), where the whole process of the optimization is efficiently conducted on a classical computer. The efficacy of the method is guaranteed by the observation that quantum circuits with a constant (or logarithmic) depth are classically tractable via simulations of local subsystems. In co-VQE, we only use quantum computers to measure nonlocal quantities after the parameters are optimized. As proof-of-concepts, we present numerical experiments on quantum spin models with topological phases. After the optimization, we identify the topological phases by nonlocal order parameters as well as unsupervised machine learning on inner products between quantum states. The proposed method maximizes the advantage of using quantum computers while avoiding strenuous optimization on noisy quantum devices. Furthermore, in terms of quantum machine learning, our study shows an intriguing approach that employs quantum computers to generate data of quantum systems while using classical computers for the learning process.

quant-ph↗

arXiv2022

Parametric t-Stochastic Neighbor Embedding With Quantum Neural Network

t-Stochastic Neighbor Embedding (t-SNE) is a non-parametric data visualization method in classical machine learning. It maps the data from the high-dimensional space into a low-dimensional space, especially a two-dimensional plane, while maintaining the relationship, or similarities, between the surrounding points. In t-SNE, the initial position of the low-dimensional data is randomly determined, and the visualization is achieved by moving the low-dimensional data to minimize a cost function. Its variant called parametric t-SNE uses neural networks for this mapping. In this paper, we propose to use quantum neural networks for parametric t-SNE to reflect the characteristics of high-dimensional quantum data on low-dimensional data. We use fidelity-based metrics instead of Euclidean distance in calculating high-dimensional data similarity. We visualize both classical (Iris dataset) and quantum (time-depending Hamiltonian dynamics) data for classification tasks. Since this method allows us to represent a quantum dataset in a higher dimensional Hilbert space by a quantum dataset in a lower dimension while keeping their similarity, the proposed method can also be used to compress quantum data for further quantum machine learning.

quant-ph↗

arXiv2022

Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers

We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the system dimension, where the interactions between divided subsystems are taken as an effective Hamiltonian expanded by the reduced basis. Then the effective Hamiltonian is further solved by VQE, which we call deep VQE. Deep VQE allows us to apply quantum-classical hybrid algorithms on small-scale quantum computers to large systems with strong intra-subsystem interactions and weak inter-subsystem interactions, or strongly correlated spin models on large regular lattices. As proof-of-principle numerical demonstrations, we use the proposed method for quasi one-dimensional models, including one-dimensionally coupled 12-qubit Heisenberg anti-ferromagnetic models on Kagome lattices as well as two-dimensional Heisenberg anti-ferromagnetic models on square lattices. The largest problem size of 64 qubits is solved by simulating 20-qubit quantum computers with a reasonably good accuracy ~ a few %. The proposed scheme enables us to handle the problems of >1000 qubits by concatenating VQEs with a few tens of qubits. While it is unclear how accurate ground state energy can be obtained for such a large system, our numerical results on a 64-qubit system suggest that deep VQE provides a good approximation (discrepancy within a few percent) and has a room for further improvement. Therefore, deep VQE provides us a promising pathway to solve practically important problems on noisy intermediate-scale quantum computers.

quant-ph↗