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

TL;DR

This paper proposes a quantum-classical hybrid system using a coherent Ising machine to optimize L0-regularization-based compressed sensing, potentially surpassing traditional L1 methods in accuracy, especially in applications like MRI.

Contribution

It introduces a novel hybrid quantum-classical approach for L0-regularized compressed sensing and provides a theoretical framework demonstrating its potential advantages.

Findings

System performance approaches the theoretical limit of compressed sensing.

Hybrid system may outperform L1-RBCS in practical data analysis.

Theoretical modeling using Wigner SDE supports the approach's effectiveness.

Abstract

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.