Mean field analysis of reverse annealing for code-division multiple-access multiuser demodulator

In this study, we evaluate the typical reverse annealing (RA) performance of the code-division multiple-access (CDMA) multiuser demodulator by means of statistical mechanics using the replica method. If we prepare for the proper initial states, first-order phase transition, which is troublesome in estimating the original signals, can be avoided or mitigated. As we increase the difficulty to obtain the ground state, further information regarding the ground state of the original problems is required to avoid first-order phase transition. In our theoretical analysis, we assume replica symmetry and static approximation. To verify our analytical results, we perform quantum Monte Carlo simulations. The analytical results are consistent with the numerical results, except for the intermediate values of the annealing parameter. Moreover, we derive the Almeida–Thouless (AT) condition for the CDMA model in RA. In our problem settings, the AT condition holds. The deviation between the analytical and numerical results is owing to the breaking of the static approximation. Thus, to investigate the effects of the static approximation, we perform RA without quantum fluctuations. In this case, the numerical results agree with the analytical results. This study is the first analytical demonstration of the application of RA to practical inference problems.