Perspectives of quantum annealing: methods and implementations

Hauke, Philipp; Katzgraber, Helmut G.; Lechner, Wolfgang; Nishimori, Hidetoshi; Oliver, William

doi:10.1088/1361-6633/ab85b8

Cited by 355 publications

(268 citation statements)

References 280 publications

Supporting

Mentioning

248

Contrasting

Unclassified

Order By: Relevance

“…Quantum simulations are emerging to be one of the important applications of quantum annealing [1][2][3][4], quite different, and arguably more natural, than the original intent of using such devices for optimization, the subject of many recent studies [5][6][7][8][9][10][11][12][13][14][15]. Prominent examples include the simulation of the Kosterlitz-Thouless topological phase transition [16,17] and three-dimensional spin glasses [18] using the D-Wave quantum annealing devices, that have successfully reproduced the behavior of various physical quantities and the structure of the phase diagram, as predicted by classical simulations.…”

Section: Introductionmentioning

confidence: 99%

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Bando

Susa

Oshiyama

et al. 2020

Phys. Rev. Research

Self Cite

120

112

View full text Add to dashboard Cite

The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors, with certain quantitative deviations from the theory likely caused by factors such as random control errors and transient effects. In addition, we probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks and their decay, and again find agreement with the quantum simulator results. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system. We support this result by extensive numerical computations. To check whether an alternative, classical interpretation of these results is possible, we used the spin-vector Monte Carlo model, a candidate classical description of the D-Wave device. We find that the degree of agreement with the experimental data from the D-Wave annealing devices is better for the KZM, a quantum theory, than for the classical spin-vector Monte Carlo model, thus favoring a quantum description of the device. Our work provides an experimental test of quantum critical dynamics in an open quantum system, and paves the way to new directions in quantum simulation experiments.

show abstract

Section: Introductionmentioning

confidence: 99%

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Bando

Susa

Oshiyama

et al. 2020

Phys. Rev. Research

Self Cite

120

112

View full text Add to dashboard Cite

show abstract

“…A major category of optimization problems, particularly amenable to D-Wave's quantum annealing, are those that can be expressed as quadratic unconstrained binary optimization (QUBO) problems. QUBO refers to a pattern matching technique, that, among other applications, can be used in machine learning and optimization, and which involves minimizing a quadratic polynomial over binary variables [20,[23][24][25][26][27][28][29]. We emphasize that QUBO is NP-hard [29].…”

Section: Qpumentioning

confidence: 99%

A QUBO Model for the Traveling Salesman Problem with Time Windows for Execution on the D-Wave

Papalitsas¹,

Andronikos²,

Giannakis³

et al. 2019

Preprint

View full text Add to dashboard Cite

This work focuses on expressing the TSP with Time Windows (TSPTW for short) as a quadratic unconstrained binary optimization (QUBO) problem. The time windows impose time constraints that a feasible solution must satisfy. These take the form of inequality constraints, which are known to be particularly difficult to articulate within the QUBO framework. This is, we believe, the first time this major obstacle is overcome and the TSPTW is cast in the QUBO formulation. We have every reason to anticipate that this development will lead to the actual execution of small scale TSPTW instances on the D-Wave platform.

show abstract

“…A major category of optimization problems, particularly amenable to D-Wave's quantum annealing, are those that can be expressed as quadratic unconstrained binary optimization (QUBO) problems. QUBO refers to a pattern matching technique that, among other applications, can be used in machine learning and optimization, and which involves minimizing a quadratic polynomial over binary variables [21,[24][25][26][27][28][29][30]. We emphasize that QUBO is NP-hard [30].…”

Section: Introductionmentioning

confidence: 99%