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

Code-division multiple-access (CDMA) multiuser detection is a kind of signal recovery problem. The main problem of CDMA multiuser detection is to estimate the original signal from the degraded information. In CDMA multiuser detection, the first-order phase transition happens. The first-order phase transition degrades the estimation performance. To avoid or mitigate the first-order phase transition, we apply adiabatic reverse annealing (ARA) to CDMA multiuser detection. In ARA, we introduce the initial Hamiltonian, which corresponds to the prior information of the original signal into quantum annealing (QA) formulation. The ground state of the initial Hamiltonian is the initial candidate solution. By using the prior information of the original signal, ARA enhances the performance of QA for CDMA multiuser detection. We evaluate the typical ARA performance of CDMA multiuser detection by means of statistical mechanics using the replica method. At first, we consider the oracle cases where the initial candidate solution is randomly generated with a fixed fraction of the original signal in the initial state. In the oracle cases, the first-order phase transition can be avoided or mitigated by ARA if we prepare for the proper initial candidate solution. We validate our theoretical analysis with quantum Monte Carlo simulations. The theoretical results to avoid the first-order phase transition are consistent with the numerical results. Next, we consider the practical cases where we prepare for the initial candidate solution obtained by commonly used algorithms. We show that the practical algorithms can exceed the threshold to avoid the first-order phase transition. Finally, we test the performance of ARA with the initial candidate solution obtained by the practical algorithm. In this case, ARA cannot avoid the first-order phase transition even if the initial candidate solution exceeds the threshold to avoid the first-order phase transition.