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arXiv:1404.2465

Quantum annealing

Alfonso de la Fuente Ruiz

Published Apr 9, 2014• 5 citations
arXivHTMLPDF

Abstract

Brief description on the state of the art of some local optimization methods: Quantum annealing Quantum annealing (also known as alloy, crystallization or tempering) is analogous to simulated annealing but in substitution of thermal activation by quantum tunneling. The class of algorithmic methods for quantum annealing (dubbed: 'QA'), sometimes referred by the italian school as Quantum Stochastic Optimization ('QSO'), is a promising metaheuristic tool for solving local search problems in multivariable optimization contexts.

DOI
10.48550/arxiv.1404.2465

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Brief description on the state of the art of some local optimization methods: Quantum annealing Quantum annealing (also known as alloy, crystallization or tempering) is analogous to simulated annealing but in substitution of thermal activation by quantum tunneling. The class of algorithmic methods for quantum annealing (dubbed: 'QA'), sometimes referred by the italian school as Quantum Stochastic Optimization ('QSO'), is a promising metaheuristic tool for solving local search problems in multivariable optimization contexts.
Quantum annealing is analogous to simulated annealing with a tunneling mechanism substituting for thermal activation. Its performance has been tested in numerical simulation with mixed conclusions. There is a class of optimization problems for which the efficiency can be studied analytically using techniques based on the statistical mechanics of spin glasses. Solving hard combinatorial problems by temperature annealing is a classic method in computer science.1) The problem is formulated in terms of a cost function, which one can identify as an energy. The dynamics are then a combination of a systematic descent in energy perturbed by a ’noise’, which is turned off gradually, inducing
Quantum annealing (QA) algorithm is a new quantum optimization algorithm based on the classical simulated annealing (SA) algorithm. Unlike classical SA algorithm, which uses the thermal waves to search for the optimal solution, the QA algorithm uses the quantum tunneling effect to allow a quantum to penetrate a potential barrier with a higher energy than itself. Therefore, the algorithm can get rid of the local extreme values and is more likely to approach the global optimal with higher probability. In the literature, the QA algorithm has shown perfect optimization effects on combinatorial optimization problems. In this paper, the basic concepts and application fields of QA algorithm, which is the core principle of D-Wave quantum computer, are systematically reviewed. The applications of QA algorithm in cryptography, traveling salesman problem, graph coloring problem, and traffic path are discussed in detail. In addition, the direction of future research for QA algorithm is explored.
We present a comparison between the Quantum Approximate Optimization Algorithm (QAOA) and two widely studied competing methods, Quantum Annealing (QA) and Simulated Annealing (SA). To achieve this, we define a class of optimization problems with respect to their spectral properties which are exactly solvable with QAOA. In this class, we identify instances for which QA and SA have an exponentially small probability to find the solution. Consequently, our results define a first demarcation line between QAOA, Simulated Annealing and Quantum Annealing, and highlight the fundamental differences between an interference-based search heuristic such as QAOA and heuristics that are based on thermal and quantum fluctuations like SA and QA respectively.
The idea of Quantum Annealing(QA),which is based on the mechanism of quantum transition tunneling effect and not same with the annealing theory of simulated thermal annealing,is a recent offspring of the celebrated simulated thermal annealing by Kirkpatrick.This paper,firstly,summarizes the basic differences between Quantum Annealing and Simulated Annealing;and then mainly addresses the attention to the practical developments of the application in optimization such as Ising spin glass,Traveling Salesman Problem,Boolean Satisfiability Problem and so on,discusses the details of the annealing process of Quantum Annealing and its compare with Simulated Annealing on test problems;subsequently,expatiates the geophysical inverse theory and method corresponding to Quantum Annealing,discusses the setting of parameters such as Temperature and Transverse field,compares the probabilities of being on configurations with different transverse fields and potential energies;finally briefly summarizes the prospects and the existent problems of using Quantum Annealing in geophysical inverse problem.