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

L0-regularization-based compressed sensing (L0-RBCS) is capable of outperforming L1-RBCS, but it is difficult to solve an optimization problem for L0-RBCS that cannot be formulated as a convex optimization. To achieve the optimization for L0-RBCS, we propose a quantum-classical hybrid system consisting of a quantum machine and a classical digital processor. Because forming a densely-connected network on a quantum machine is required for solving this problem, the coherent Ising machine (CIM) is one of suitable quantum machines for composing this hybrid system. To evaluate theoretically the performance of the CIM-classical hybrid system, a truncated Wigner stochastic differential equation (W-SDE) is obtained from the master equation for the density operator of the network of degenerate optical parametric oscillators, and macroscopic equations are derived from the W-SDE using statistical mechanics. We show that the system performance in principle approaches the theoretical limit of compressed sensing and in practical situations this hybrid system can exceed L1-RBCSs estimation accuracy.

Emergent limits of an indirect measurement from phase transitions of inference

Measurements are inseparable from inference, where the estimation of signals of interest from other observations is called an indirect measurement. While a variety of measurement limits have been defined by the physical constraint on each setup, the fundamental limit of an indirect measurement is essentially the limit of inference. Here, we propose the concept of statistical limits on indirect measurement: the bounds of distinction between signals and noise and between a signal and another signal. By developing the asymptotic theory of Bayesian regression, we investigate the phenomenology of a typical indirect measurement and demonstrate the existence of these limits. Based on the connection between inference and statistical physics, we also provide a unified interpretation in which these limits emerge from phase transitions of inference. Our results could pave the way for novel experimental design, enabling assess to the required quality of observations according to the assumed ground truth before the concerned indirect measurement is actually performed.