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This study aimed to investigate the evolutionary dynamics of a three-strategy game that combines snowdrift and stag hunt games. This game is motivated by an experimental study, which found that individual solution lowers cooperation levels. Agents adopting this option aim to address a problem to the extent necessary to remove negative impact on themselves, although they do not free ride on cooperation effort provided by others. This property of the individual solution is similar to that of option defection in the stag hunt. Thus, the role of the interplay of defection in the snowdrift game and individual solution was examined in this study. The well-mixed population has two asymptotically stable rest points, one wherein the individual solution occupies the population, and the other wherein cooperation and defection coexist. The interactions on a square lattice enlarge the parameter region wherein cooperation survives, and the three strategies often coexist. The scrutinization of the evolutionary process shows that multiple mechanisms lead to the coexistence of the three strategies depending on parameter values. Our analysis suggests that considering the individual solution adds complexity to the evolutionary process, which might contribute to our understanding on the evolution of cooperation., Comment: 10 pages, 6 figures

Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules in 5-state CA with any ergodic and periodic boundary condition, and numerically confirm all the other rules non-ergodic with some boundary condition. We classify ergodic rules into several patterns, which exhibit a variety of ergodic structure., Comment: 63 pages, 47 figures

The preferential treatment of in-group members is widely observed. This study examines this phenomenon in the domain of cooperation in social dilemmas using evolutionary agent-based models that consider the role of partner selection. The model considers a repeated prisoner's dilemma game, in which agents belong to one of two groups that are distinguished by the continuation probability of pair interactions. On the basis of the behavior in the last round and the group affiliation of the partner, each individual selects to cooperate, defect, or stop interactions and search for a different partner. The results of simulation demonstrated that agents adopt cooperative strategies, including tit-for-tat and out-for-tat, toward in-group members. By contrast, agents stop interactions immediately after pair formation without observing their partner's behavior when they are paired with an out-group individual. Higher continuation probability with in-group partners hinders interaction with out-group individuals. Our results imply the importance of avoidance in intergroup interactions in social dilemmas and might explain in-group favoritism without enmity toward out-groups., Comment: 10 pages, 5 figures; (supplementary materials: 4 pages, 4 figures)

A coherent XY machine (CXYM) is a physical spin simulator that can simulate the XY model by mapping XY spins onto the continuous phases of non-degenerate optical parametric oscillators (NOPOs). Here, we demonstrated a large-scale CXYM with >47,000 spins by generating 10-GHz-clock time-multiplexed NOPO pulses via four-wave mixing in a highly nonlinear fiber inside a fiber ring cavity. By implementing a unidirectional coupling from the i-th pulse to the (i+1)-th pulse with a variable 1-pulse delay planar lightwave circuit interferometer, we successfully controlled the effective temperature of a one-dimensional XY spin network within two orders of magnitude., Comment: 5 pages, 4 figures

Multipartite entanglement is a critical resource in quantum information processing that exhibits much richer phenomenon and stronger correlations than in bipartite systems. This advantage is also reflected in its multi-user applications. Although many demonstrations have used photonic polarization qubits, polarization-mode dispersion confines the transmission of photonic polarization qubits through an optical fiber. Consequently, time-bin qubits have a particularly important role to play in quantum communication systems. Here, we generate a three-photon time-bin Greenberger-Horne-Zeilinger (GHZ) state using a 2 x 2 optical switch as a time-dependent beam splitter to entangle time-bin Bell states from a spontaneous parametric down-conversion source and a weak coherent pulse. To characterize the three-photon time-bin GHZ state, we performed measurement estimation, showed a violation of the Mermin inequality, and used quantum state tomography to fully reconstruct a density matrix, which shows a state fidelity exceeding 70%. We expect that our three-photon time-bin GHZ state can be used for long-distance multi-user quantum communication., Comment: 8 pages, 4 figures, 1 table

We generated time-multiplexed degenerate optical parametric oscillator (DOPO) pulses using a nonlinear fiber Sagnac loop as a phase-sensitive amplifier (PSA) where the pump and amplified light in pump-signal-idler degenerate four-wave mixing can be spatially separated. By placing the PSA in a fiber cavity, we successfully generated more than 5,000 time-multiplexed DOPO pulses. We confirmed the bifurcation of pulse phases to 0 or $\pi$ relative to the pump phase, which makes them useful for representing Ising spins in an Ising model solver based on coherent optical oscillator networks. We also confirmed inherent randomness of the DOPO phases using the NIST random number test., Comment: 5 pages, 3 figures, 1 table

This study considers a variant of the bounded confidence opinion formation model wherein the probability of opinion assimilation is dependent on the relative similarity of opinions. Agents are located on a social network and decide whether or not they adopt the opinion of one of the neighbors (called a role agent). Opinion assimilation is more (less) likely to occur when the distance from the opinion of the role agent is smaller (larger) than the average opinion distance from other neighbors. Thus, assimilation probability is reliant not only on opinion proximity with the role agent considered in conventional models but also on relative similarity that considers other neighbors. The simulation results demonstrate that large weights on relative similarity in determining assimilation probability increase the size of the largest opinion cluster. The size of the threshold parameter of the bounded confidence model displays inverse-U relationships with the largest cluster size. The findings imply that consideration of relative opinion similarity, as observed in recent empirical studies, prevents polarization into small opinion clusters., Comment: 8 pages, 6 figures

Noisy mean field annealing (NMFA) is an algorithm that mimics a coherent Ising machine (CIM), which is an optical system for solving Ising problems. The NMFA has reproduced the solver performance of the CIM for systems of limited size even though it simplifies the interaction between spins with a mean-field approximation. However, recent experiments observing various thermodynamic quantities have revealed that the CIM can capture the phase transitions of the two-dimensional Ising models that the mean field cannot capture. This situation leads to a fundamental question as to how well the NMFA can capture the features of the thermodynamic quantities around the phase transition. This paper answers that the NMFA reproduces the thermodynamic features of the mean field, but cannot reproduce the CIM results. This suggests that, in terms of sampling, the level of performance of the CIM is beyond that of the NMFA., Comment: 6 pages, 6 figures

A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the spin sets sampled by the CIM can be regarded as a canonical ensemble, we estimate the effective temperature of the spins represented by degenerate optical parametric oscillator pulses by using maximum likelihood estimation. With the obtained temperature, we confirmed that the thermodynamic quantities obtained with the CIM exhibited a phase-transition-like behavior that better matches the analytical and numerical results than the mean field one., Comment: 6 pages, 3 figures

In the "Beyond Moore's Law" era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore's Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries., Comment: 80 pages accepted in Nano Futures

Non-orthogonal multiple access (NOMA) technique is important for achieving a high data rate in next-generation wireless communications. A key challenge to fully utilizing the effectiveness of the NOMA technique is the optimization of the resource allocation (RA), e.g., channel and power. However, this RA optimization problem is NP-hard, and obtaining a good approximation of a solution with a low computational complexity algorithm is not easy. To overcome this problem, we propose the coherent Ising machine (CIM) based optimization method for channel allocation in NOMA systems. The CIM is an Ising system that can deliver fair approximate solutions to combinatorial optimization problems at high speed (millisecond order) by operating optimization algorithms based on mutually connected photonic neural networks. The performance of our proposed method was evaluated using a simulation model of the CIM. We compared the performance of our proposed method to simulated annealing, a conventional-NOMA pairing scheme, deep Q learning based scheme, and an exhaustive search scheme. Simulation results indicate that our proposed method is superior in terms of speed and the attained optimal solutions., Comment: 16 pages, 10 figures. This work has been submitted to the IEEE for possible publication

We experimentally demonstrate that networks of identical photonic spiking neurons based on coupled degenerate parametric oscillators can show various chimera states, in which, depending on their local synchronization and desynchronization, different kinds of spiking dynamics can develop in a self-organized manner. Even when only a static interaction is implemented, through synchronized inputs from connected neurons, the spiking mode of photonic neurons can be spontaneously and adaptively changed between the Class-I and Class-II modes classified by A. L. Hodgkin. This spontaneous spiking-mode shift induces a significant change in the spiking frequency despite the all neurons having the same natural spiking frequency, which encourages the generation of chimera states. Controllability and self-organized flexibility of the spiking modes in the present system allow us to create an experimental platform to explore the nature of chimera states in neuromorphic spiking neural networks., Comment: 26 pages, 12 figures

A high-dimensional quantum key distribution (QKD) can improve error rate tolerance and the secret key rate. Many $d$-dimensional QKDs have used two mutually unbiased bases (MUBs), while $(d+1)$ MUBs enable a more robust QKD, especially against correlated errors. However, a scalable implementation has not been achieved because the setups have required $d$ devices even for two MUBs or a flexible convertor for a specific optical mode. Here, we propose a scalable and general implementation of $(d+1)$ MUBs using $\log_p d$ interferometers in prime power dimensions $d=p^N$. We implemented the setup for time-bin states and observed an average error rate of 3.8% for phase bases, which is lower than the 23.17% required for a secure QKD against coherent attack in $d=4$., Comment: 7 pages, 3 figures, followed by Supplemental Material of 11 pages, 2 figure, 2 table

Processes of individual attitude formation and their macroscopic consequences have become an intriguing research topic, and agent-based models of opinion formation have been proposed to understand this phenomenon. This study conducted an agent-based simulation and examined the role of mass media in a noisy opinion formation process, where opinion heterogeneity is preserved by a weak intensity of assimilation and errors accompanying opinion modifications. In a computational model, agents conformed to their neighbours' opinions in social networks. In addition, each agent tended to be influenced by one of a two external agents with fixed opinions, that is, mass media that take opposite positions on an opinion spectrum. The simulation results demonstrated that a small probability of interactions with mass media reduces opinion heterogeneity even with extreme mass media position values. However, a large frequency of interactions with mass media increases opinion heterogeneity. Accordingly, intermediate assimilation strength achieves the least heterogeneous opinion distribution. The influence of mass media dampens the effects of network topology. Our simulation implies that mass media can play qualitatively different roles depending on their positions and intensity of influence., Comment: 9 pages, 9 figures

Nonlinear dynamics of spiking neural networks has recently attracted much interest as an approach to understand possible information processing in the brain and apply it to artificial intelligence. Since information can be processed by collective spiking dynamics of neurons, the fine control of spiking dynamics is desirable for neuromorphic devices. Here we show that photonic spiking neurons implemented with paired nonlinear optical oscillators can be controlled to generate two modes of bio-realistic spiking dynamics by changing the optical pump amplitude. When they are coupled in a network, we found that the interaction between the photonic neurons induces an effective change in the pump amplitude depending on the order parameter that characterizes synchronization. The experimental results show that the effective change causes spontaneous modification of the spiking modes and firing rates of clustered neurons, and such collective dynamics can be utilized to realize efficient heuristics for solving NP-hard combinatorial optimization problems., Comment: 43 pages, 9 figures

Understanding the role of network structure in the evolution of cooperation is a key research goal at the intersection between physics and biology. Recent studies have particularly focused on multiplex networks given that multiple social domains are interrelated and cannot be represented by single-layer networks. However, the role of network multiplexity is not fully understood when combined with another important network characteristic: network dynamics. In the present study, we investigated evolutionary prisoner's dilemma games played on dynamic two-layer multiplex networks in which the payoff combined across the two layers determined strategy evolution. In addition, we introduced network dynamics where agents can sever links with defecting neighbors and construct new links. Our simulation showed that link updating enhances cooperation but the resultant states are far from those of full cooperation. This modest enhancement in cooperation was related to symmetry breaking whereby the cooperation frequency in one layer disproportionately increased while that in the other layer remained the same or even diminished. However, this broken symmetry disappeared with sufficiently fast link updating. Our results show that the introduction of network dynamics enhances cooperation in the prisoner's dilemma as previously reported, but this enhancement is accompanied by significant asymmetry once network multiplexity is considered., Comment: 13 pages, 14 figures, 1 table; updated on the basis of reviewers' comments

Frequency translation of single photons while preserving their quantum characteristics is an important technology for flexible networking of photonic quantum communication systems. Here we demonstrate a flexible scheme to interface different-color photons using an optical single sideband (OSSB) modulator. By changing the radio-frequency signal that drives the modulators, we can easily shift and precisely tune the frequency of single photons. Using the OSSB modulator, we successfully erased the frequency distinguishability of non-degenerated photon pairs to obtain the Hong-Ou-Mandel interference with a visibility exceeding 90%. We also demonstrated that the level of distinguishability can be precisely controlled by the OSSB modulator. We expect that the OSSB modulator will provide a simple and flexible photonic interface for realizing advanced quantum information systems.

Quantum logic gates are important for quantum computations and quantum information processing in numerous physical systems. While time-bin qubits are suited for quantum communications over optical fiber, many essential quantum logic gates for them have not yet been realized. Here, we demonstrated a controlled-phase (C-Phase) gate for time-bin qubits that uses a 2x2 optical switch based on an electro-optic modulator. A Hong-Ou-Mandel interference measurement showed that the switch could work as a time-dependent beam splitter with a variable spitting ratio. We confirmed that two independent time-bin qubits were entangled as a result of the C-Phase gate operation with the switch.