  We propose a quantum-classical hybrid system consisting of coherent Ising
machines (CIM) and classical digital processors, which performs alternating
minimization for L0 regularization-based compressed sensing (CS). A truncated
Wigner stochastic differential equation (W-SDE) is obtained from the master
equation for the density operator of the network of degenerate optical
parametric oscillators. The macroscopic equations in statistical mechanics are
derived from the W-SDE to evaluate theoretically the performance of CIM L0
regularization-based CS. We show that the system performance in principle
approaches the theoretical limit of L0 minimization-based CS derived by
Nakanishi et al. (2016) and possibly exceeds that of the least absolute
shrinkage and selection operator (LASSO). We also conduct numerical experiments
confirming that in practical situations this hybrid system can exceed LASSO's
estimation accuracy.
