L0 regularization-based compressed sensing with quantum–classical hybrid approach. (1st July 2022)

• Record Type: Journal Article
• Authors: Aonishi, Toru; Mimura, Kazushi; Okada, Masato; Yamamoto, Yoshihisa
• Is Part Of: Quantum science and technology. Volume 7:Number 3(2022)
• Publication Date: 2022-07-01
• Subjects: quantum machine -- coherent Ising machine -- compressed sensing -- magnetic resonance imaging -- quantum–classical hybrid system -- LASSO -- non-equilibrium statistical mechanics; Quantum theory -- Periodicals; Quantum theory; Periodicals; 530
• DOI: 10.1088/2058-9565/ac6f19
• Languages: English
• ISSNs: 2058-9565

Abstract

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.