AQC 2016 - Avoiding Negative Sign Problem in Simulation of Quantum Annealilng

A Google TechTalk, June 29, 2016, presented by Masayuki Ohzeki (Kyoto University) ABSTRACT: We invent a novel technique to implement the XX-type interaction, which exhibits the negative sign problem in the standard way of the quantum Monte-Carlo simulation, as well as the transverse field. The method utilizes the auxiliary transverse field which adaptively changes its strength according to the value of the transverse magnetization. Our proposed method enables us to perform the quantum Monte-Carlo simulation for various models and implement Belief Propagation in quantum spin models. The former paves a way to simulate the quantum annealing in wider range of the quantum fluctuations. The latter provides another way to exploits the quantum fluctuation in the various computer science problems as the error-correcting codes, signal processing, compressed sensing, machine learning and so on. We confirms the validity of our method in the simple model with the anti-ferro magnetic interactions in x directions and the mean-field analysis of the Gaussian-noise channel model (CDMA) with the transverse field and so on. In the future, we aim at observation of the boundary between the limitation of the classical and quantum computations via our method. Presented at the Adiabatic Quantum Computing Conference, June 26-29, 2016, at Google's Los Angeles office.