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IEEE Journal of Quantum Electronics

Performance Dependence of Optical-Loop-Based Coherent Ising Machine on Operating Conditions

Kyo Inoue, Shogo Kitahara, Koji Igarashi

Published Jun 25, 2025• 0 citations
Publisher

Abstract

Coherent Ising machines (CIMs) are optical computers designed to solve combinatorial optimization problems based on the Ising model. Among several variants, the optical-loop-based CIM, which utilizes optical pulses with binary phases circulating in a loop equipped with a pulse-pumped phase-sensitive amplifier (PSA) and a measurement feedback circuit, has experimentally demonstrated high performance in terms of the number of pulses and connectivity. This study numerically investigates the dependence of its calculation performance on operating conditions such as the noise level, coupling strength between pulses, and PSA pump increment rate. The CIM solving Max-Cut problems is simulated using a difference equation based on a traveling-wave model under various operating conditions. The results indicate that noise is not a critical factor, there is an optimal condition for the coupling strength, depending on the graph structure, and slower pump-increment rate leads to higher scores. Under optimal conditions, the simulation produces better calculation results than those previously reported in an experimental study.

DOI
10.1109/jqe.2025.3583102

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Coherent Ising machines (CIMs) are optical computers designed to solve combinatorial optimization problems based on the Ising model. Among several variants, the optical-loop-based CIM, which utilizes optical pulses with binary phases circulating in a loop equipped with a pulse-pumped phase-sensitive amplifier (PSA) and a measurement feedback circuit, has experimentally demonstrated high performance in terms of the number of pulses and connectivity. This study numerically investigates the dependence of its calculation performance on operating conditions such as the noise level, coupling strength between pulses, and PSA pump increment rate. The CIM solving Max-Cut problems is simulated using a difference equation based on a traveling-wave model under various operating conditions. The results indicate that noise is not a critical factor, there is an optimal condition for the coupling strength, depending on the graph structure, and slower pump-increment rate leads to higher scores. Under optimal conditions, the simulation produces better calculation results than those previously reported in an experimental study.
The coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs) that solves for the ground state of Ising problems through OPO bifurcation dynamics. Here, we present experimental results comparing the performance of the CIM to quantum annealers (QAs) on two classes of NP-hard optimization problems: ground state calculation of the Sherrington-Kirkpatrick (SK) model and MAX-CUT. While the two machines perform comparably on sparsely-connected problems such as cubic MAX-CUT, on problems with dense connectivity, the QA shows an exponential performance penalty relative to CIMs. We attribute this to the embedding overhead required to map dense problems onto the sparse hardware architecture of the QA, a problem that can be overcome in photonic architectures such as the CIM.
Coherent Ising machines (CIMs) have emerged as a hybrid form of quantum computing devices designed to solve NP-complete problems, offering an exciting opportunity for discovering optimal solutions. Despite challenges such as susceptibility to noise-induced local minima, we achieved notable advantages in improving the computational accuracy and stability of CIMs. We conducted a successful experimental demonstration of CIM via femtosecond laser pumping that integrates optimization strategies across optical and structural dimensions, resulting in significant performance enhancements. The results are particularly promising. An average success rate of 55% was achieved to identify optimal solutions within a Möbius Ladder graph comprising 100 vertices. Compared with other alternatives, the femtosecond pulse results in significantly higher peak power, leading to more pronounced quantum effects and lower pump power in optical fiber-based CIMs. In addition, we have maintained an impressive success rate for a continuous period of 8 hours, emphasizing the practical applicability of CIMs in real-world scenarios. Furthermore, our research extends to the application of these principles in practical applications such as molecular docking and credit scoring. The results presented substantiate the theoretical promise of CIMs, paving the way for their integration into large-scale practical applications.
Coherent Ising machines (CIMs) are increasingly anticipated as a new computer that can solve combinatorial optimization problems. CIMs use degenerate optical parametric oscillator pulses as artificial spins. We constructed a 100,512-spin coherent Ising machine, the world's largest. Our CIM can find good solutions to maximum cut problems of 100,000-node graphs ~1000 times faster than simulated annealing. Furthermore, it provides both very good scores and a broad distribution when we operate it near the phase transition point.
Coherent Ising Machines (CIMs) have emerged as a hybrid form of quantum computing devices designed to solve NP-complete problems, offering an exciting opportunity for discovering optimal solutions. Despite challenges such as susceptibility to noise-induced local minima, we achieved notable advantages in improving the computational accuracy and stability of CIMs. We conducted a successful experimental demonstration of CIM via femto-second laser pumping that integrates optimization strategies across optical and structural dimensions, resulting in significant performance enhancements. The results are particularly promising. An average success rate of 55% was achieved to identify optimal solutions within a Mobius Ladder graph comprising 100 vertices. Compared with other alternatives, the femto-second pulse results in significantly higher peak power, leading to more pronounced quantum effects and lower pump power in optical fiber based CIMs. In addition, we have maintained an impressive success rate for a continuous period of 8 hours, emphasizing the practical applicability of CIMs in real-world scenarios. Furthermore, our research extends to the application of these principles in practical applications such as molecular docking and credit scoring. The results presented substantiate the theoretical promise of CIMs, paving the way for their integration into large-scale practical applications.
Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative approach to solve these problems by a specialized physical computing system. To evaluate its potential performance, computational experiments are performed on maximum cut (MAX-CUT) problems against traditional algorithms such as semidefinite programming relaxation of Goemans-Williamson and simulated annealing by Kirkpatrick, et al. The numerical results empirically suggest that the almost constant computation time is required to obtain the reasonably accurate solutions of MAX-CUT problems on a CIM with the number of vertices up to 2×1042 \times 10^42×104 and the number of edges up to 10810^8108.
Abstract A Coherent Ising machine (CIM) is an oscillator-network-based analog computing system to circumvent the bottleneck in von Neumann digital computing architectures. The CIM consists of a network of degenerate optical parametric oscillators (DOPOs) and is designed to find a ground state or perform Boltzmann sampling for all degenerate ground states and low-energy excited states in combinatorial optimization problems. A nonlinear measurement feedback scheme, called chaotic amplitude control (CAC), has recently been proposed to correct pulse amplitude inhomogeneity and thereby faithfully map the Ising Hamiltonian to the loss landscape of the DOPO network. However, the quantum limit of the CIM-CAC performance is not fully explored yet. This work clarifies how the quantum noise squeezing and the measurement-induced state shift in repeated indirect quantum measurements improve the system performance. From the numerical simulation on the Ising model with the Zeeman terms, obtained from combinatorial clustering problems formulated as constrained optimization problems, it is revealed that the CIM-CAC operating in a single photon per pulse regime dramatically outperforms the standard CIM-CAC with a large photon number per pulse. This is because the standard CIM-CAC is often trapped in a periodic trajectory and cannot escape from there. On the other hand, the significant improvement is brought by the noise-induced amplitude jump in the single photon CIM-CAC.