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Tomoki Yamagami

Publications and source records attributed to Tomoki Yamagami.

14 recordsLinked to original sources
arXiv2026

Hadamard Rigidity of Positive Sojourn Time Distributions for Rotation Coins

We study the distribution of the positive sojourn time for a one-dimensional two state quantum walk, conditioned on return to the origin. Konno showed that, for the Hadamard walk, this conditional distribution is exactly uniform at times divisible by $4$. In this paper, we investigate whether this finite time exact uniformity characterizes the Hadamard coin within the family of rotation coins. For a fixed initial state, we prove that the following three conditions are equivalent for rotation coins: the conditional distribution is exactly uniform at time $8$; the conditional distribution is exactly uniform at every time $4m$ with $m\ge2$; and the coin is the Hadamard coin. Thus, the uniformity phenomenon found by Konno is characterized as a rigidity phenomenon of the Hadamard coin within the rotation coin family. The proof uses a matrix-valued generating function for paths returning to the origin. We analyze the algebraic structure arising from an absorbing process on the half line. Finally, by comparing low degree coefficients at time $8$, we show that exact uniformity forces the rotation coin to be the Hadamard coin.

quant-ph↗
arXiv2026

Photonic reservoir computing with complex networks

Photonic reservoir computing has attracted increasing attention as a fast and low-cost approach for time-series prediction. Photonic reservoir computing utilizes the high speed, broad bandwidth, and spatial parallelism of light. However, the effect of the internal connection structure (network topology) on the computing performance has not been investigated for large-scale photonic reservoirs. In this study, we experimentally and numerically demonstrate photonic reservoir computing using a spatial light modulator to systematically evaluate the relationship between the network topology and the performance of reservoir computing. We introduce complex network structures such as small-world and scale-free network topologies of the internal nodes in the reservoir. We perform the memory capacity measurement and the one-step-ahead prediction task of the chaotic time series to compare the performance. We found that the small-world network exhibits the maximum memory capacity and the best prediction performance. Our numerical calculations reveal that the performance of the time-series prediction can be optimized by changing the rewiring probability of the network and the leak rate of the reservoir. We also implement photonic human brain network as a reservoir, which is designed by the connectomes of human brain activities. We found that the network topology strongly affects the performance of reservoir computing, and the small-world network structure outperforms the other configurations.

physics.optics↗
arXiv2026

Autocorrelation effects in a stochastic-process model for solving two-armed bandit problems

Decision makers exploiting photonic chaotic dynamics obtained by semiconductor lasers provide an ultrafast approach to solving multi-armed bandit problems by using a temporal optical signal as the driving source for sequential decisions. In such systems, the sampling interval of the chaotic waveform shapes the temporal correlation of the resulting time series, and experiments have reported that decision accuracy depends strongly on this autocorrelation property. However, it remains unclear whether the benefit of autocorrelation can be explained by a minimal mathematical model. Here, we analyze a stochastic-process model for solving the two-armed bandit problem based on time series, where the threshold and a two-valued Markov signal evolve jointly. Numerical results reveal an environment-dependent structure: negative (positive) autocorrelation is optimal in reward-rich (reward-poor) environments. These findings show that negative autocorrelation of the time series is advantageous when the sum of the winning probabilities is more than one, whereas positive autocorrelation is useful when the sum of the winning probabilities is less than one. Moreover, the performance is independent of autocorrelation if the sum of the winning probabilities equals one, which is mathematically clarified. This study paves the way for solving the two-armed bandit problems for reinforcement learning applications in wireless communications and robotics.

cs.LG↗
arXiv2025

Quantum spatial best-arm identification via quantum walks

Quantum reinforcement learning has emerged as a framework combining quantum computation with sequential decision-making, and applications to the multi-armed bandit (MAB) problem have been reported. The graph bandit problem extends the MAB setting by introducing spatial constraints, where the accessibility of arms is restricted by graph connectivity, yet quantum approaches to this setting remain limited. In this paper, we formulate best-arm identification in graph bandits and propose a quantum algorithmic framework, termed Quantum Spatial Best-Arm Identification (QSBAI), which is applicable to general graph structures. This framework uses quantum walks to encode superpositions over graph-constrained actions, thereby extending amplitude amplification and generalizing the quantum BAI algorithm via Szegedy's walk framework. We focus our theoretical analysis on complete and bipartite graphs, deriving the maximal success probability of identifying the best arm and the time step at which it is achieved. Our results clarify how quantum-walk-based search can be adapted to structurally constrained decision problems and provide a foundation for quantum best-arm identification in graph-structured environments.

quant-ph↗
arXiv2025

Multi-player conflict avoidance through entangled quantum walks

Quantum computing has the potential to solve complex problems faster and more efficiently than classical computing. It can achieve speedups by leveraging quantum phenomena like superposition, entanglement, and tunneling. Quantum walks (QWs) form the foundation for many quantum algorithms. Unlike classical random walks, QWs exhibit quantum interference, leading to unique behaviors such as linear spreading and localization. These properties make QWs valuable for various applications, including universal computation, time series prediction, encryption, and quantum hash functions. One emerging application of QWs is decision making. Previous research has used QWs to model human decision processes and solve multi-armed bandit problems. This paper extends QWs to collective decision making, focusing on minimizing decision-conflict cases where multiple agents choose the same option, leading to inefficiencies like traffic congestion or overloaded servers. Prior research using quantum interference has addressed two-player conflict avoidance but struggled with three-player scenarios. This paper proposes a novel method using QWs to entirely eliminate decision conflicts in three-player cases, demonstrating its effectiveness in collective decision making.

quant-ph↗
arXiv2025

A study of the Antlion Random Walk

Random walks (RWs) are fundamental stochastic processes with applications across physics, computer science, and information processing. A recent extension, the laser chaos decision-maker, employs chaotic time series from semiconductor lasers to solve multi-armed bandit (MAB) problems at ultrafast speeds, and its threshold adjustment mechanism has been modeled as an RW. However, previous analyses assumed complete memory preservation ($\alpha = 1$), overlooking the role of partial memory in balancing exploration and exploitation. In this paper, we introduce the Antlion Random Walk (ARW), defined by $X_t = \alpha X_{t-1} + \xi_t$ with $\alpha \in [0,1]$ and Rademacher-distributed increments $(\xi_t)$, which describes a walker pulled back toward the origin before each step. We show that varying $\alpha$ significantly alters ARW dynamics, yielding distributions that range from uniform-like to normal-like. Through mathematical and numerical analyses, we investigate expectation, variance, reachability, positive-side residence time, and distributional similarity. Our results place ARWs within the framework of autoregressive (AR(1)) processes while highlighting distinct non-Gaussian features, thereby offering new theoretical insights into memory-aware stochastic modeling of decision-making systems.

math.PR↗
arXiv2023

Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk

Quantum walks (QWs) have a property that classical random walks (RWs) do not possess -- the coexistence of linear spreading and localization -- and this property is utilized to implement various kinds of applications. This paper proposes RW- and QW-based algorithms for multi-armed-bandit (MAB) problems. We show that, under some settings, the QW-based model realizes higher performance than the corresponding RW-based one by associating the two operations that make MAB problems difficult -- exploration and exploitation -- with these two behaviors of QWs.

quant-ph↗
arXiv2023

Asymmetric quantum decision-making

Collective decision-making is crucial to information and communication systems. Decision conflicts among agents hinder the maximization of potential utilities of the entire system. Quantum processes can realize conflict-free joint decisions among two agents using the entanglement of photons or quantum interference of orbital angular momentum (OAM). However, previous studies have always presented symmetric resultant joint decisions. Although this property helps maintain and preserve equality, it cannot resolve disparities. Global challenges, such as ethics and equity, are recognized in the field of responsible artificial intelligence as responsible research and innovation paradigm. Thus, decision-making systems must not only preserve existing equality but also tackle disparities. This study theoretically and numerically investigates asymmetric collective decision-making using quantum interference of photons carrying OAM or entangled photons. Although asymmetry is successfully realized, a photon loss is inevitable in the proposed models. The available range of asymmetry and method for obtaining the desired degree of asymmetry are analytically formulated.

quant-ph↗
arXiv2023

Skeleton structure inherent in discrete-time quantum walks

In this paper, we claim that a common underlying structure--a skeleton structure--is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the initial state, and partially, even of the coin matrix. This structure is best interpreted in the context of quantum-walk-replicating random walks (QWRWs), i.e., random walks that replicate the probability distribution of quantum walks, where this newly found structure acts as a simplified formula for the transition probability. Additionally, we construct a random walk whose transition probabilities are defined by the skeleton structure and demonstrate that the resultant properties of the walkers are similar to both the original QWs and QWRWs.

math-ph↗
arXiv2023

Information-theoretical analysis of statistical measures for multiscale dynamics

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as clocks and lasers, ranging from short to long time scales. Although these two statistical measures were developed independently for different purposes in different fields in the literature, their interest is to examine multiscale temporal structures of physical phenomena under study. We show that, from an information-theoretical perspective, they share some foundations and exhibit similar tendencies. We experimentally confirmed that similar properties of the MSE and Allan variance can be observed in low-frequency fluctuations (LFF) in chaotic lasers and physiological heartbeat data. Furthermore, we calculated the condition under which this consistency between the MSE and Allan variance exists, which is related to certain conditional probabilities. Heuristically, physical systems in nature including the aforementioned LFF and heartbeat data mostly satisfy this condition, and hence the MSE and Allan variance demonstrate similar properties. As a counterexample, an artificially constructed random sequence is demonstrated, for which the MSE and Allan variance exhibit different trends.

nlin.CD↗
arXiv2022

Directivity of quantum walk via its random walk replica

Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as quantum-walk-replicating random walks (QWRWs), have been studied in the literature where the eventual properties of QWRW coincide with those of QWs. However, we consider that the unique attributes of QWRWs have not been fully utilized in the former studies to obtain deeper or new insights into QWs. In this paper, we highlight the directivity of one-dimensional discrete quantum walks via QWRWs. By exploiting the fact that QWRW allows trajectories of individual walkers to be considered, we first discuss the determination of future directions of QWRWs, through which the effect of linear spreading and localization is manifested in another way. Furthermore, the transition probabilities of QWRWs can also be visualized and show a highly complex shape, representing QWs in a novel way. Moreover, we discuss the first return time to the origin between RWs and QWs, which is made possible via the notion of QWRWs. We observe that the first return time statistics of QWs are quite different from RWs, caused by both the linear spreading and localization properties of QWs.

math-ph↗
arXiv2022

Theory of Acceleration of Decision Making by Correlated Time Sequences

Photonic accelerators have been intensively studied to provide enhanced information processing capability to benefit from the unique attributes of physical processes. Recently, it has been reported that chaotically oscillating ultrafast time series from a laser, called laser chaos, provide the ability to solve multi-armed bandit (MAB) problems or decision-making problems at GHz order. Furthermore, it has been confirmed that the negatively correlated time-domain structure of laser chaos contributes to the acceleration of decision-making. However, the underlying mechanism of why decision-making is accelerated by correlated time series is unknown. In this study, we demonstrate a theoretical model to account for accelerating decision-making by correlated time sequence. We first confirm the effectiveness of the negative autocorrelation inherent in time series for solving two-armed bandit problems using Fourier transform surrogate methods. We propose a theoretical model that concerns the correlated time series subjected to the decision-making system and the internal status of the system therein in a unified manner, inspired by correlated random walks. We demonstrate that the performance derived analytically by the theory agrees well with the numerical simulations, which confirms the validity of the proposed model and leads to optimal system design. The present study paves the way for improving the effectiveness of correlated time series for decision-making, impacting artificial intelligence and other applications.

cs.LG↗
arXiv2021

General condition of quantum teleportation by one-dimensional quantum walks

We extend the scheme of quantum teleportation by quantum walks introduced by Wang et al. (2017). First, we introduce the mathematical definition of the accomplishment of quantum teleportation by this extended scheme. Secondly, we show a useful necessary and sufficient condition that the quantum teleportation is accomplished rigorously. Our result classifies the parameters of the setting for the accomplishment of the quantum teleportation.

quant-ph↗