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arXiv:2108.07369 · Advanced Quantum Technologies

Coherent Ising Machines with Optical Error Correction Circuits

Sam Reifenstein, Satoshi Kako, Farad Khoyratee, Timothee G. Leleu, Y. Yamamoto

Published Sep 7, 2021• 46 citations

Abstract

Abstract A coherent Ising machine (CIM) comprising a network of open‐dissipative quantum oscillators with optical error correction circuits is proposed. In the proposed network, the squeezed/anti‐squeezed vacuum states of the constituent optical parametric oscillators establish quantum correlations below the threshold through optical mutual coupling and 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 optical error correction feedback. The particular algorithm used by the proposed network is derived from the truncated Wigner stochastic differential equation. As an optical hardware technology, the proposed CIM has several unique features, including programmable all‐to‐all Ising coupling in the optical domain, directional coupling ()‐induced chaotic behavior, and the ability to operate at low power at room temperature. The proposed CIM is evaluated in terms of its performance and how this scales at different problem sizes. It is shown that the various CIMs discussed in this paper are effective at solving many problem types, although the optimal algorithm depends on the problem case. It is further shown that the proposed optical implementations can be achieved with low energy consumption on thin‐film LiNbO 3 platforms.

DOI: 10.1002/qute.202100077

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A coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs), in which the “strongest” collective mode of oscillation at well above threshold corresponds to an optimum solution of a given Ising problem. When a pump rate or network coupling rate is increased from below to above threshold, however, the eigenvectors with the smallest eigenvalue of the Ising coupling matrix [Jij] appear near threshold and impede the machine to relax to true ground states. Two complementary approaches to attack this problem are described here. One approach is to utilize the squeezed/anti-squeezed vacuum noise of OPOs below threshold to produce coherent spreading over numerous local minima via quantum noise correlation, which could enable the machine to access either true ground states or excited states with eigen-energies close enough to that of ground states above threshold. The other approach is to implement a real-time error correction feedback loop so that the machine migrates from one local minimum to another during an explorative search for ground states. Finally, a set of qualitative analogies connecting the CIM and traditional computer science techniques are pointed out. In particular, belief propagation and survey propagation used in combinatorial optimization are touched upon.

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Abstract Squeezed vacuum state of light is an important concept of quantum optics which has an uncertainty reduction in a specific quadrature compared to the coherent vacuum state. The coherent Ising machines (CIMs) based on the squeezed state are capable of searching the ground state of the Ising model, which can be used to solve combinatorial optimization problems and have been experimentally demonstrated to have excellent computational performance. This review introduces the recent progress of a CIM hardware solver based on optical parametric oscillators, including the delayed optical path scheme and a measurement feedback scheme. Also, the basic principles, unique advantages, and potential challenges are described. We expect that the applications of large-scale CIM hardware solvers will have a huge impact on the acceleration of the computation power.

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.

We report a coherent Ising machine (CIM), which is a network of degenerate optical parametric oscillators for simulating the Ising model. Using a long-distance fiber cavity that includes a telecom-band phase sensitive amplifier, we generated large number of degenerate optical parametric oscillator (DOPO) pulses multiplexed in time domain, which represent the Ising spins. By using a measurement and feedback scheme, we could implement all-to-all coupling among 2048 DOPOs. We experimentally confirmed that the CIM could find solutions to maximum cut problems for graphs with as many as 2000 nodes.