  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.
