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Mathematical foundation of quantum annealing
Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantumExpand
Quantum Spin Liquid in Spin 1/2 J1–J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and thoseExpand
Convergence theorems for quantum annealing
We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular, theExpand
Distributed dynamic weaving is a crosscutting concern
This paper proposes our new language named DandyJ, which enables developers to implement distributed dynamic weaving by an aspect, which is also a crosscutting concern. Expand
Tensor renormalization group with randomized singular value decomposition.
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensionalExpand
Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
We investigate the first-order phase transitions of the $q$-state Potts models with $q = 5, 6, 7$, and $8$ on the two-dimensional square lattice, using Monte Carlo simulations. At the very weaklyExpand
Calculation of higher-order moments by higher-order tensor renormalization group
A calculation method for higher-order moments of physical quantities, including magnetization and energy, based on the higher- order tensor renormalization group is proposed. Expand
Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
We numerically study Heisenberg models on modified triangular lattices, and show that a weak next-nearest-neighbor exchange interaction added to a simple triangular lattice, namely, the equilateralExpand
mVMC - Open-source software for many-variable variational Monte Carlo method
We introduce more than ten thousands variational parameters and simultaneously optimize them by using the stochastic reconfiguration (SR) method. Expand
Variational Monte Carlo method in the presence of spin-orbit interaction and its application to Kitaev and Kitaev-Heisenberg models
We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interactions. The algorithm is applicable even in a wider class of Hamiltonians that do notExpand