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Register a new userCoherent Ising machines -- Quantum optics and neural network perspectives
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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 a smallest eigenvalue of Ising coupling matrix [J_ij] 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 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 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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The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators (OPOs) and a field programmable gate array (FPGA) circuit. The similar mathematical models were proposed three decades ago by J. J. Hopfield, et al. in the context of classical neural networks. In this article, we compare the computational performance of both models.
A new technique is demonstrated for carrying out exact positive-P phase-space simulations of the coherent Ising machine quantum computer. By suitable design of the coupling matrix, general hard optimization problems can be solved. Here, quantum simulations of a feedback type of photonic parametric network are carried out, which is the implementation of the coherent Ising machine. Results for success rates are obtained using a weighted algorithm for quantum simulations of quantum feedback devices.
We present the quantum theory of coherent Ising machines based on networks of degenerate optical parametric oscillators (DOPOs). In a simple model consisting of two coupled DOPOs, both positive-$P$ representation and truncated Wigner representation predict quantum correlation and inseparability between the two DOPOs in spite of the open-dissipative nature of the system. Here, we apply the truncated Wigner representation method to coherent Ising machines with thermal, vacuum, and squeezed reservoir fields. We find that the probability of finding the ground state of a one-dimensional Ising model increases substantially as a result of reducing excess thermal noise and squeezing the incident vacuum fluctuation on the out-coupling port.
In this survey, various generalisations of Glauber-Sudarshan coherent states are described in a unified way, with their statistical properties and their possible role in non-standard quantisations of the classical electromagnetic field. Some statistical photon-counting aspects of Perelomov SU(2) and SU(1,1) coherent states are emphasized.
Ising machines use physics to naturally guide a dynamical system towards an optimal state which can be read out as a heuristical solution to a combinatorial optimization problem. Such designs that use nature as a computing mechanism can lead to higher performance and/or lower operation costs. Quantum annealers are a prominent example of such efforts. However, existing Ising machines are generally bulky and energy intensive. Such disadvantages might lead to intrinsic advantages at some larger scale in the future. But for now, integrated electronic designs allow more immediate applications. We propose one such design that uses bistable nodes, coupled with programmable and variable strengths. The design is fully CMOS compatible for on-chip applications and demonstrates competitive solution quality and significantly superior execution time and energy.
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