  L0-regularization-based compressed sensing (L0-RBCS) has the potential to
outperform L1-regularization-based compressed sensing (L1-RBCS), but the
optimization in L0-RBCS is difficult because it is a combinatorial optimization
problem. To perform optimization in L0-RBCS, we propose a quantum-classical
hybrid system consisting of a quantum machine and a classical digital
processor. The coherent Ising machine (CIM) is a suitable quantum machine for
this system because this optimization problem can only be solved with a densely
connected network. To evaluate the performance of the CIM-classical hybrid
system theoretically, a truncated Wigner stochastic differential equation
(W-SDE) is introduced as a model for the network of degenerate optical
parametric oscillators, and macroscopic equations are derived by applying
statistical mechanics to the W-SDE. We show that the system performance in
principle approaches the theoretical limit of compressed sensing and this
hybrid system may exceed the estimation accuracy of L1-RBCS in actual
situations, such as in magnetic resonance imaging data analysis.
