# Effective implementation of $l_0$-Regularised Compressed Sensing with Chaotic-Amplitude-Controlled Coherent Ising Machines

## TL;DR

This paper demonstrates that a closed-loop chaotic-amplitude-controlled coherent Ising machine improves the accuracy and effectiveness of $l_0$-regularised compressed sensing compared to open-loop systems, using optical and MRI data.

## Contribution

It introduces a closed-loop CIM with chaotic amplitude control for enhanced $l_0$-regularised compressed sensing, surpassing open-loop system performance.

## Key findings

- Improved accuracy over open-loop systems.
- Wider effectiveness range demonstrated.
- Validated with artificial and MRI data.

## Abstract

Coherent Ising Machine (CIM) is a network of optical parametric oscillators that can solve large-scale combinatorial optimisation problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et al., proposed a quantum-classical hybrid system to solve optimisation problems of $l_0$-regularisation-based compressed sensing. In the hybrid system, the CIM was an open-loop system without an amplitude control feedback loop. In this case, the hybrid system is enhanced by using a closed-loop CIM to achieve chaotic behaviour around the target amplitude, which would enable escaping from local minima in the energy landscape. Both artificial and magnetic resonance image data were used for the testing of our proposed closed-loop system. Compared with the open-loop system, the results of this study demonstrate an improved degree of accuracy and a wider range of effectiveness.