Coupled Quantum Fluctuations and Quantum Annealing

優也 関, Yuya Seki, 秀稔 西森 +1 more

友紀 須佐, Yuki Susa, 秀稔 西森 +2 more

洋介 大坪

This thesis provides theoretical studies on a probabilistic information processing incorporated quantum fluctuations through statistical mechanical approaches.Quantum fluctuations cause transitions between states, which play same role as thermal fluctuations.Such an idea has been used in optimization problems for searching a ground state of a cost function.The algorithm is called quantum annealing (QA) in a manner analogous to simulated annealing.Simulated annealing is the conventional algorithm for finding the ground state by using the thermal fluctuations.QA has been applied to various optimization problems by solving the Schrödinger equation or carrying out Quantum Monte Carlo simulations on classical computers.However, what we call a quantum annealer with current superconducting devices has been launched by D-wave systems.For this situation, the algorithms by using the quantum fluctuations have received a lot of attention in recent years.With the developments in the research fields of the algorithms by making use of the quantum fluctuations, it is also interesting for us to consider the possible application of the quantum fluctuations to probabilistic information processing.Main problem of the probabilistic information processing in the context of this thesis is to recover the original information from damaged information, e.g., image restoration, error correcting codes, and CDMA multiuser demodulation.Such problems can be denoted as the infiniterange spin glass model, adopting the framework of Bayesian statistics.Then, we can apply statistical mechanical approaches to it in order to figure out the average-case performance of those systems.We examine the average-case performance of the probabilistic information processing in which quantum fluctuations is utilized to recover the original information in the context of the Bayesian inference.The quantum fluctuations are built into the system as transverse fields put in the infinite-range Ising spin glass model.We evaluate the performance measurement by using statistical mechanics which mean mean-field theory.Accordingly, we find the following properties on the quantum fluctuations in the probabilistic information processing

秀稔 西森, Hidetoshi Nishimori

Shu Tanaka

Quantum annealing method has been widely attracted attention in statistical physics and information science since it is expected to be a powerful method to obtain the best solution of optimization problem as well as simulated annealing. The quantum annealing method was incubated in quantum statistical physics. This is an alternative method of the simulated annealing which is well-adopted for many optimization problems. In the simulated annealing, we obtain a solution of optimization problem by decreasing temperature (thermal fluctuation) gradually. In the quantum annealing, in contrast, we decrease quantum field (quantum fluctuation) gradually and obtain a solution. In this paper we review how to implement quantum annealing and show some quantum fluctuation effects in frustrated Ising spin systems.

Wade DeGottardi, David Ferguson, С. А. Новиков +2 more