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

• URL: http://arxiv.org/abs/2102.11412v5
• Date: Fri, 6 May 2022 12:57:07 GMT
• Title: L0 regularization-based compressed sensing with quantum-classical hybrid approach
• Authors: Toru Aonishi, Kazushi Mimura, Masato Okada, Yoshihisa Yamamoto
• Abstract summary: We propose a quantum-classical hybrid system consisting of a quantum machine and a classical digital processor. We show that the system may exceed the estimation accuracy of L1-RBCS in actual situations.
• Score: 2.2710740436620314
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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