Study on Quantum Annealing Using the Density Matrix Renormalization Group

Abstract

Quantum annealing is a quantum algorithm proposed recently for combinatorial optimization problems. It manipulates time evolution of a quantum mechanical state and obtain an approximate solution. In order to implement the algorithm in classical computers, we propose to apply the density matrix renormalization group method. Simulation of the time evolution of a quantum mechanical state becomes possible by the density matrix renormalization group method for problems of large size. We explain quantum annealing and the density matrix renormalization group method, and present results of numerical simulation using them.

Coherent quantum annealing in a programmable 2000-qubit Ising chain

“…Matrix product state and density matrix renormalization group methods have recently been employed for the modeling of annealing dynamics in one dimensional systems consisting of a transverse-field Ising model coupled to a bosonic bath at both zero and finite temperatures, for both finite systems and the infinite system limit [28,[56][57][58][59]. Coupling to the bosonic bath is handled by use of a quasi-adiabatic path integral (QUAPI) method [60,61].…”

A Method to Change Phase Transition Nature — Toward Annealing Methods

“…There are many types of implementation methods of the quantum annealing, for example, quantum Monte Carlo simulation, realtime dynamics, and time-dependent density matrix renormalization group (t-DMRG). 53,54 Here we focus on the quantum annealing using the realtime evolution which will be explained in Appendix B.…”

Hybrid Quantum Annealing for Clustering Problems

“…The second one is based on a time-dependent density matrix renormalization group. 15,16 By this method, we can study time-evolution of one-dimensional quantum systems. However it is difficult to treat two-dimensional or three-dimensional quantum systems by this method.…”