Efficient quantum and simulated annealing of Potts models using a half-hot constraint

The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time required to obtain the ground states by simulated annealing exponentially increases with the system size. This study analytically confirms that the transverse magnetic-field quantum annealing induces a first-order phase transition. This result implies that quantum annealing does not exponentially accelerate the ground-state search of the ferromagnetic Potts model. To avoid the first-order phase transition, we propose an iterative optimization method using a half-hot constraint that is applicable to both quantum and simulated annealing. In the limit of $Q \to \infty$, a saddle point equation under the half-hot constraint is identical to the equation describing the behavior of the fully connected ferromagnetic Ising model, thus confirming a second-order phase transition. Furthermore, we verify the same relation between the fully connected Potts glass model and the Sherrington--Kirkpatrick model under assumptions of static approximation and replica symmetric solution. The proposed method is expected to obtain low-energy states of the Potts models with high efficiency using Ising-type computers such as the D-Wave quantum annealer and the Fujitsu Digital Annealer.Comment: 16 pages, 10 figure

Bayesian Reconstruction of Missing Observations

We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framework of Bayesian reconstruction and its application to the traffic data reconstruction problem in the field of traffic engineering. In the latter part of this paper, we describe the evaluation of the statistical performance of our Bayesian traffic reconstruction model using a statistical mechanical approach and clarify its statistical behavior

Weak axioms of determinacy and subsystems of analysis II (∑02 games)

AbstractIn [10], we have shown that the statement that all ∑11 partitions are Ramsey is deducible over ATR0 from the axiom of ∑11 monotone inductive definition,but the reversal needs П11-CA0 rather than ATR0. By contrast, we show in this paper that the statement that all ∑02 games are determinate is also deducible over ATR0 from the axiom of ∑11 monotone inductive definition, but the reversal is provable even in ACA0. These results illuminate the substantial differences among lightface theorems which can not be observed in boldface