Abstract
The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large-scale optimization problems because of its scalability and high-speed computational ability. The CIM is a non-equilibrium open-dissipative system, so the theories and techniques of classical equilibrium thermodynamics cannot be directly applied to it. Our research group has adapted these theories and techniques to work with the CIM. Here, we focus on an infinite loading Hopfield model, which is a canonical frustrated model of Ising computation. We derive a macroscopic equation to elucidate the relation between critical memory capacity and normalized pump rate in the CIM-implemented Hopfield model.
Highlights
Machine learning algorithms have recently been used to tackle problems in the big data field. Many of these algorithms can be formulated as large optimizations that are mapped to Ising computing problems in which the goal is to find the ground state of an Ising Hamiltonian
We develop a statistical mechanics method based on self-consistent signal-to-noise a)Electronic mail: aonishi@c.titech.ac.jp analysis (SCSNA)11,12 and derive macroscopic equations for the infinite loading Hopfield model implemented in the coherent Ising machine (CIM)
We succeeded in deriving macroscopic equations for the infinite-loading Hopfield model composed of degenerate optical parametric oscillator (DOPO) and used them to analyze the memory capacity of the model for different values of the normalized pump rate p, coupling-strength parameter J, and normalization constant As
Summary
Machine learning algorithms have recently been used to tackle problems in the big data field Many of these algorithms can be formulated as large optimizations that are mapped to Ising computing problems in which the goal is to find the ground state of an Ising Hamiltonian. The mutually coupled DOPO pulses can be approximately modeled with the following c-number stochastic differential equations (CSDEs): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dci dt 1⁄4. The CSDE looks like a classical statistical model but is fully equivalent to the exact quantum theory based on the density operator master equation and describes various quantum features of CIM such as quantum entanglement formation.. J is a coupling-strength parameter, which is normalized by the system size, i.e., the number of DOPO pulses N, as is done with the connections of the. It is technically difficult to create an injection field larger than the c-amplitude of each DOPO pulse in actual CIM equipment.
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