Search

In recent years, quantum Ising machines have drawn a lot of attention, but due to physical implementation constraints, it has been difficult to achieve dense coupling, such as full coupling with sufficient spins to handle practical large-scale applications. Consequently, classically computable equations have been derived from quantum master equations for these quantum Ising machines. Parallel implementations of these algorithms using FPGAs have been used to rapidly find solutions to these problems on a scale that is difficult to achieve in physical systems. We have developed an FPGA implemented cyber coherent Ising machine (cyber CIM) that is much more versatile than previous implementations using FPGAs. Our architecture is versatile since it can be applied to the open-loop CIM, which was proposed when CIM research began, to the closed-loop CIM, which has been used recently, as well as to Jacobi successive over-relaxation method. By modifying the sequence control code for the calculation control module, other algorithms such as Simulated Bifurcation (SB) can also be implemented. Earlier research on large-scale FPGA implementations of SB and CIM used binary or ternary discrete values for connections, whereas the cyber CIM used FP32 values. Also, the cyber CIM utilized Zeeman terms that were represented as FP32, which were not present in other large-scale FPGA systems. Our implementation with continuous interaction realizes N=4096 on a single FPGA, comparable to the single-FPGA implementation of SB with binary interactions, with N=4096. The cyber CIM enables applications such as CDMA multi-user detector and L0 compressed sensing which were not possible with earlier FPGA systems, while enabling superior calculation speeds, more than ten times faster than a GPU implementation. The calculation speed can be further improved by increasing parallelism, such as through clustering., Comment: 20 pages, 9 figures

Coherent Ising Machine (CIM) is a network of optical parametric oscillators that solves combinatorial optimization problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et al. proposed a quantum-classical hybrid system to solve optimization problems of L0-regularization-based compressed sensing (L0RBCS). Gunathilaka et al. has further enhanced the accuracy of the system. However, the computationally expensive CIM's stochastic differential equations (SDEs) limit the use of digital hardware implementations. As an alternative to Gunathilaka et al.'s CIM SDEs used previously, we propose using the mean-field CIM (MF-CIM) model, which is a physics-inspired heuristic solver without quantum noise. MF-CIM surmounts the high computational cost due to the simple nature of the differential equations (DEs). Furthermore, our results indicate that the proposed model has similar performance to physically accurate SDEs in both artificial and magnetic resonance imaging data, paving the way for implementing CIM-based L0RBCS on digital hardware such as Field Programmable Gate Arrays (FPGAs)., Comment: 19 pages, 7 figures

Coherent Ising Machine (CIM) is a network of optical parametric oscillators that solves combinatorial optimization problems by finding the ground state of an Ising Hamiltonian. In CIMs, a problem arises when attempting to realize the Zeeman term because of the mismatch in size between interaction and Zeeman terms due to the variable amplitude of the optical parametric oscillator pulses corresponding to spins. There have been three approaches proposed so far to address this problem for CIM, including the absolute mean amplitude method, the auxiliary spin method, and the chaotic amplitude control (CAC) method. This paper focuses on the efficient implementation of Zeeman terms within the mean-field CIM model, which is a physics-inspired heuristic solver without quantum noise. With the mean-field model, computation is easier than with more physically accurate models, which makes it suitable for implementation in field programmable gate arrays (FPGAs) and large-scale simulations. Firstly, we examined the performance of the mean-field CIM model for realizing the Zeeman term with the CAC method, as well as their performance when compared to a more physically accurate model. Next, we compared the CAC method to other Zeeman term realization techniques on the mean-field model and a more physically accurate model. In both models, the CAC method outperformed the other methods while retaining similar performance., Comment: 8 pages, 4 figures

Coherent Ising Machine (CIM) is a network of optical parametric oscillators that can solve large-scale combinatorial optimisation problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et al., proposed a quantum-classical hybrid system to solve optimisation problems of $l_0$-regularisation-based compressed sensing. In the hybrid system, the CIM was an open-loop system without an amplitude control feedback loop. In this case, the hybrid system is enhanced by using a closed-loop CIM to achieve chaotic behaviour around the target amplitude, which would enable escaping from local minima in the energy landscape. Both artificial and magnetic resonance image data were used for the testing of our proposed closed-loop system. Compared with the open-loop system, the results of this study demonstrate an improved degree of accuracy and a wider range of effectiveness., Comment: 35 pages, 12 figures

We propose a network of open-dissipative quantum oscillators with optical error correction circuits. In the proposed network, the squeezed/anti-squeezed vacuum states of the constituent optical parametric oscillators below the threshold establish quantum correlations through optical mutual coupling, while collective symmetry breaking is induced above the threshold as a decision-making process. This initial search process is followed by a chaotic solution search step facilitated by the optical error correction feedback. As an optical hardware technology, the proposed coherent Ising machine (CIM) has several unique features, such as programmable all-to-all Ising coupling in the optical domain, directional coupling $(J_{ij} \neq J_{ji})$ induced chaotic behavior, and low power operation at room temperature. We study the performance of the proposed CIMs and investigate how the performance scales with different problem sizes. The quantum theory of the proposed CIMs can be used as a heuristic algorithm and efficiently implemented on existing digital platforms. This particular algorithm is derived from the truncated Wigner stochastic differential equation. We find that the various CIMs discussed are effective at solving many problem types, however the optimal algorithm is different depending on the instance. We also find that the proposed optical implementations have the potential for low energy consumption when implemented optically on a thin film LiNbO3 platform.

We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the D\"urr-Hoyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover's search. We use MaxCut problems as our reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. We empirically observe a $\Theta(2^{\sqrt{n}})$ scaling for the median TTS for MFB-CIM, in comparison to the exponential scaling with the exponent $n$ for DAQC and the provable $\widetilde{\mathcal O}\left(\sqrt{2^n}\right)$ scaling for DH-QMF. We conclude that these scaling complexities result in a dramatic performance advantage for MFB-CIM in comparison to the other two algorithms for solving MaxCut problems., Comment: 24 pages, 20 figures

We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising model. We formulate a general discrete-time Gaussian-state model of the MFB-CIM which faithfully captures the nonlinear dynamics present at and above system threshold. This model overcomes the limitations of both mean-field models, which neglect quantum noise, and continuous-time models, which assume long photon lifetimes. Numerical simulations of our model show that when the MFB-CIM is operated in a quantum-noise-dominated regime with short photon lifetimes (i.e., low cavity finesse), homodyne monitoring of the system can efficiently produce samples of low-energy Ising spin configurations, requiring many fewer roundtrips to sample than suggested by established high-finesse, continuous-time models. We find that sampling performance is robust to, or even improved by, turning off or altogether reversing the sign of the parametric drive, but performance is critically reduced in the absence of optical nonlinearity. For the class of MAX-CUT problems with binary-signed edge weights, the number of roundtrips sufficient to fully sample all spin configurations up to the first-excited Ising energy, including all degeneracies, scales as $1.08^N$. At a problem size of $N = 100$ with a few dozen (median of 20) such desired configurations per instance, we have found median sufficient sampling times of $6\times10^6$ roundtrips; in an experimental implementation of an MFB-CIM with a 10 GHz repetition rate, this corresponds to a wall-clock sampling time of 60 ms., Comment: The first two authors contributed equally to this work. 24 pages, 9 figures

A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial optimization problems. However, there are two challenges in the previously proposed approach: (1) The machine can be trapped by local minima which increases exponentially with problem size and (2) the machine fails to map a target Hamiltonian correctly on the loss landscape of a neural network due to oscillator amplitude heterogeneity. Both of them lead to erroneous solutions rather than correct answers. In this paper, we show that it is possible to overcome these two problems partially but simultaneously by introducing error detection and correction feedback mechanism. The proposed machine achieves efficient sampling of degenerate ground states and low-energy excited states via its inherent migration property during a solution search process., Comment: 12 pages, 7 figures

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., Comment: 12 pages, 5 figures, 1 table (main text); 14 pages, 12 figures, 2 tables (supplementary)

We present measurements of the second-order coherence function on emission from single GaN quantum dots. In some cases a large degree of photon antibunching is observed, demonstrating isolation of a single quantum system. For a selected quantum dot, we study the dependence of photon antibunching on excitation power and temperature. Using pulsed excitation, we demonstrate an ultraviolet triggered single-photon source operating at a wavelength of 358 nm., Comment: 3 pages, 4 figures