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L0-regularization-based compressed sensing (L0-RBCS) has the potential tooutperform L1-regularization-based compressed sensing (L1-RBCS), but theoptimization in L0-RBCS is difficult because it is a combinatorial optimizationproblem. To perform optimization in L0-RBCS, we propose a quantum-classicalhybrid system consisting of a quantum machine and a classical digitalprocessor. The coherent Ising machine (CIM) is a suitable quantum machine forthis system because this optimization problem can only be solved with a denselyconnected network. To evaluate the performance of the CIM-classical hybridsystem theoretically, a truncated Wigner stochastic differential equation(W-SDE) is introduced as a model for the network of degenerate opticalparametric oscillators, and macroscopic equations are derived by applyingstatistical mechanics to the W-SDE. We show that the system performance inprinciple approaches the theoretical limit of compressed sensing and thishybrid system may exceed the estimation accuracy of L1-RBCS in actualsituations, such as in magnetic resonance imaging data analysis.

L0 regularization-based compressed sensing with quantum-classical hybrid approach