arXiv subjects

Kensuke Inaba

Publications and source records attributed to Kensuke Inaba.

At least 19 recordsLinked to original sources

arXiv2026

Penalty-Free Two-Step Optimization of Higher-Order Ising Problems for Two-Dimensional Line-Controlled RIS

Reconfigurable intelligent surfaces (RISs) are often assumed to allow continuous phase control over all elements, leading to hardware cost that scales with the number of elements. Treating the phase of each element as a discrete variable is essential for improving cost effectiveness toward ubiquitous RIS deployment. However, the resulting discrete optimization problem is inherently difficult to solve. To address this challenge, this letter proposes a two-dimensional line-control method to reduce the degrees of freedom of the phase variables. The formulation yields a fourth-order objective function and is not directly compatible with physical optimizers such as coherent Ising machines and quantum annealers, which are designed for quadratic interactions. Conventional methods for reducing the order of the objective function with additional auxiliary variables increase the number of variables and require additional penalty parameters, limiting scalability. We therefore propose a two-step optimization method that transforms the fourth-order objective into two successive quadratic optimization problems. For a RIS with 5,476 elements, the required number of discrete variables is reduced from 11,100 to 5,476. Experiments using a real coherent Ising machine demonstrated that the proposed approach solved the discrete-phase optimization problem with 5,476 elements, while limiting the beamforming-gain loss to 2 dB compared with the full continuous-control case.

eess.SP↗

arXiv2026

Scalable and Near-Optimal Discrete Phase Shift Optimization for Reconfigurable Intelligent Surfaces with Over 20,000 Elements

This paper proposes a novel optimization framework for discrete phase shifts of a reconfigurable intelligent surface (RIS) using a coherent Ising machine (CIM). Unlike conventional methods based on iterative convex approximation or combinatorial search with exponentially increasing complexity, the CIM physically explores the solution space of Ising Hamiltonians through collective mode competition in a network of optical oscillators, enabling efficient large-scale discrete optimization. We formulate the RIS discrete phase optimization problem as a quadratic Ising model, which supports both binary and quaternary phase shifts by appropriately mapping quantized phase states to spin variables. Using a real hardware CIM, we experimentally solve quadratic optimization problems for RISs with up to 22,201 elements. The results demonstrate that the proposed method achieves physically consistent beam patterns under both line-of-sight and non-line-of-sight environments and attains the theoretical gain when transitioning from binary to quaternary phase shift. To further enhance scalability, we introduce a spin-size reduction approach that removes spins deterministically fixed by dominant channel components. This technique efficiently reduces the problem size for CIM in line-of-sight conditions without performance loss. These results confirm that CIM-based optimization offers a practical and highly scalable solution for large RIS deployments with discrete phase shift constraints.

cs.IT↗

arXiv2023

10-GHz-clock time-multiplexed non-degenerate optical parametric oscillator network with a variable planar lightwave circuit interferometer

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.

physics.optics↗

arXiv2023

Detecting partial synchrony in a complex oscillatory network using pseudo-vortices

Partial synchronization is characteristic phase dynamics of coupled oscillators on various natural and artificial networks, which can remain undetected due to the complexity of the systems. With an analogy between pairwise asynchrony of oscillators and topological defects, i.e., vortices, in the two-dimensional XY spin model, we propose a robust and data-driven method to identify the partial synchronization on complex networks. The proposed method is based on an integer matrix whose element is pseudo-vorticity that discretely quantifies asynchronous phase dynamics in every two oscillators, which results in graphical and entropic representations of partial synchrony. As a first trial, we apply our method to 200 FitzHugh-Nagumo neurons on a complex small-world network. Partially synchronized chimera states are revealed by discriminating synchronized states even with phase lags. Such phase lags also appear in partial synchronization in chimera states. Our topological, graphical, and entropic method is implemented solely with measurable phase dynamics data, which will lead to a straightforward application to general oscillatory networks including neural networks in the brain.

cond-mat.dis-nn↗

arXiv2023

Thermodynamic quantities of two-dimensional Ising models obtained by noisy mean field annealing and coherent Ising machine

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.

cond-mat.stat-mech↗

arXiv2023

Observing a Phase Transition in a Coherent Ising Machine

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.

cond-mat.stat-mech↗

arXiv2022

High-Speed Resource Allocation Algorithm Using a Coherent Ising Machine for NOMA Systems

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.

cs.IT↗

arXiv2022

Experimental observation of chimera states in spiking neural networks based on degenerate optical parametric oscillators

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.

physics.optics↗

arXiv2020

Collective and synchronous dynamics of photonic spiking neurons

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.

physics.optics↗

arXiv2018

Experimental Determination of Bose-Hubbard Energies

We present the first experimental measurement of the ensemble averages of both the kinetic and interaction energies of the three-dimensional Bose--Hubbard model at finite temperature and various optical lattice depths across weakly to strongly interacting regimes, for an almost unit filling factor. The kinetic energy is obtained through Fourier transformation of a time-of-flight signal, and the interaction energy is measured using a newly developed atom-number-projection spectroscopy technique, by exploiting an ultra-narrow optical transition of two-electron atoms. The obtained experimental results can be used as benchmarks for state-of-the-art numerical methods of quantum many-body theory. As an illustrative example, we compare the measured energies with numerical calculations involving the Gutzwiller and cluster-Gutzwiller approximations, assuming realistic trap potentials and particle numbers at nonzero entropy (finite temperature); we obtain good agreement without fitting parameters. We also discuss the possible application of this method to temperature estimations for atoms in optical lattices using the thermodynamic relation. This study offers a unique advantage of cold atom system for `quantum simulators', because, to the best of our knowledge, it is the first experimental determination of both the kinetic and interaction energies of quantum many-body system.

cond-mat.quant-gas↗

arXiv2018

Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer

Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems. Here, we study the performance of two types of annealing machines--a commercially available quantum annealer built by D-Wave Systems, and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillator networks--on two classes of problems, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on regular graphs of degree 3. On denser problems, however, we observe an exponential penalty for the quantum annealer ($\exp(-\alpha_\textrm{DW} N^2)$) relative to CIMs ($\exp(-\alpha_\textrm{CIM} N)$) for fixed anneal times, on both the SK model and on 50%-edge-density MAX-CUT, where the coefficients $\alpha_\textrm{CIM}$ and $\alpha_\textrm{DW}$ are problem-class-dependent. On instances with over $50$ vertices, a several-orders-of-magnitude time-to-solution difference exists between CIMs and the D-Wave annealer. An optimal-annealing-time analysis is also consistent with a significant projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the measurement-feedback facilitated all-to-all connectivity of the CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.

quant-ph↗

arXiv2016

Topological defect formation in 1D and 2D spin chains realized by network of optical parametric oscillators

A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this "Ising machine" for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice, and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear "growth stage" and a nonlinear "saturation stage". These predictions are compared against recent data for a 10,000-spin 1D Ising machine.

physics.optics↗

arXiv2016

Large-scale Ising spin network based on degenerate optical parametric oscillators

Simulating a network of Ising spins with physical systems is now emerging as a promising approach for solving mathematically intractable problems. Here we report a large-scale network of artificial spins based on degenerate optical parametric oscillators (DOPO), paving the way towards a photonic Ising machine capable of solving difficult combinatorial optimization problems. We generated >10,000 time-division-multiplexed DOPOs using dual-pump four-wave mixing (FWM) in a highly nonlinear fibre (HNLF) placed in a fibre cavity. Using those DOPOs, a one-dimensional (1D) Ising model was simulated by introducing nearest-neighbour optical coupling. We observed the formation of spin domains and found that the domain size diverged near the DOPO threshold, which suggests that the DOPO network can simulate the behavior of low-temperature Ising spins.

physics.optics↗

arXiv2015

BCS superconducting transitions in lattice fermions

We develop a general description of the superconductivity of lattice fermions based on the BCS theory. We propose a modeling of the density of states (DOS) of lattice fermions, where divergent and semi-metallic structures are described by asymptotic expansions around the Fermi energy. This modeling leads to a unified representation of the transition temperature $T_c$ at half filling, which reproduces asymptotic forms of $T_c$ derived in several lattices, such as the square, honeycomb, and Lieb lattices, for the weakly interacting limit. The derived asymptotic forms of $T_c$ are categorized into four types, which is attributed to the different responses of the degenerate fermions depending on the DOS structures. The DOS with a delta-functional singularity induces the highest $T_c$ in the weakly interacting region, where $T_c$ is linearly proportional to the pairing interaction $U$. Three kinds of universal ratios defined in the BCS theory no longer reduce to constants independent of the system parameters but can be parameterized with a certain variable that characterizes the singular structures of the DOS. We find universal relationship among thermodynamic quantities that holds for all parameter regions. Further, we numerically demonstrate that in multi-band systems the correlation effects can induce an effective delta-functional singularity. This phenomenon generally appears in multi-energy (or multi-gap) systems and may provide a plausible guideline for material designs of high-$T_c$ superconductor.

cond-mat.supr-con↗

arXiv2015

Theoretical Analysis on Spectroscopy of Atomic Bose-Hubbard Systems

We provide a numerical method to calculate comprehensively the microwave and the laser spectra of ultracold bosonic atoms in optical lattices at finite temperatures. Our formulation is built up with the sum rules, up to the second order, derived from the general principle of spectroscopy. The sum rule approach allows us to discuss the physical origins of a spectral peak shift and also a peak broadening. We find that a spectral broadening of superfluid atoms can be determined from number fluctuations of atoms, while that of normal-state atoms is mainly attributed to quantum fluctuations resulting from hopping of atoms. To calculate spectra at finite temperatures, based on the sum rule approach, we provide a two-mode approximation assuming that spectra of the superfluid and normal state atoms can be calculated separately. Our method can properly deal with multi-peak structures of spectra resulting from thermal fluctuations and also coexisting of the superfluid and the normal states. By combining the two-mode approximation with a finite temperature Gutzwiller approximation, we calculate spectra at finite temperatures by considering realistic systems, and the calculated spectra show nice agreements with those in experiments.

cond-mat.quant-gas↗

arXiv2015

Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities

We describe the enhanced magnetic transition temperatures $T_c$ of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold atom experiments. We determine the phase diagram at half-filling using the dynamical mean-field theory. The dominant mechanism of enhanced $T_c$ gradually changes from the (delta-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures.

cond-mat.quant-gas↗

arXiv2014

Flat-band ferromagnetism in the multilayer Lieb optical lattice

We theoretically study magnetic properties of two-component cold fermions in half-filled multilayer Lieb optical lattices, i.e., two, three, and several layers, using the dynamical mean-field theory. We clarify that the magnetic properties of this system become quite different depending on whether the number of layers is odd or even. In odd-number-th layers in an odd-number-layer system, finite magnetization emerges even with an infinitesimal interaction. This is a striking feature of the flatband ferromagnetic state in multilayer systems as a consequence of the Lieb theorem. In contrast, in even-number layers, magnetization develops from zero on a finite interaction. These different magnetic behaviours are triggered by the flat bands in the local density of states and become identical in the limit of the infinite-layer (i.e., three-dimensional) system. We also address how interlayer hopping affects the magnetization process. Further, we point out that layer magnetization, which is a population imbalance between up and down atoms on a layer, can be employed to detect the emergence of the flat-band ferromagnetic state without addressing sublattice magnetization.

cond-mat.quant-gas↗

arXiv2014

Three-body losses of repulsively interacting three-component fermionic atoms in optical lattices

We investigate the effects of a repulsive three-body interaction on the Mott transition of the repulsively interacting three-component fermionic atoms in optical lattices by means of the self-energy functional approach. We find that the three-body repulsion hardly affects the qualitative features of the Mott transition, because the three-body repulsion does not compete with the two-body repulsions. When the three-body repulsion is extremely strong, the triple occupancy vanishes in the Fermi liquid state. This situation is equivalent to that caused by strong three-body losses. Our results imply that three-body losses have little influence on the Mott transitions in the repulsively interacting three-component fermionic atoms in optical lattices.

cond-mat.quant-gas↗