A quantum walk-assisted approximate algorithm for bounded NP optimisation problems

This paper describes an application of the quantum approximate optimisation algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution...

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Bibliographic Details
Published in:Quantum information processing Vol. 18; no. 3; pp. 1 - 18
Main Authors: Marsh, S., Wang, J. B.
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2019
Springer Nature B.V
Subjects:
Algorithms
Computer simulation
Data Structures and Information Theory
Mathematical Physics
Optimization
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Minimum vertex cover
Quantum walks
Quantum optimisation
QAOA
ISSN:1570-0755, 1573-1332
Online Access:Get full text
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Summary:This paper describes an application of the quantum approximate optimisation algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution to alternating quantum walks and solution-quality-dependent phase shifts and use the quantum walks to integrate the problem constraints of NPO problems. We apply the concept of a hybrid quantum-classical variational scheme to attempt finding the highest expectation value, which contains a high-quality solution. We synthesise an efficient quantum circuit for the constrained optimisation algorithm, and we numerically demonstrate the behaviour of the circuit with respect to an illustrative NP optimisation problem with constraints, minimum vertex cover. With examples, this paper demonstrates that the degree of accuracy to which the quantum walks are simulated can be treated as an additional optimisation parameter, leading to improved results.
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ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-019-2171-3