### Abstract

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.

Original language | English |
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Article number | 61 |

Journal | Quantum Information Processing |

Volume | 18 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2019 |

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*Quantum Information Processing*, vol. 18, no. 3, 61. https://doi.org/10.1007/s11128-019-2171-3

**A quantum walk-assisted approximate algorithm for bounded NP optimisation problems.** / Marsh, S.; Wang, J. B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A quantum walk-assisted approximate algorithm for bounded NP optimisation problems

AU - Marsh, S.

AU - Wang, J. B.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - 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.

AB - 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.

KW - Minimum vertex cover

KW - QAOA

KW - Quantum optimisation

KW - Quantum walks

UR - http://www.scopus.com/inward/record.url?scp=85060326012&partnerID=8YFLogxK

U2 - 10.1007/s11128-019-2171-3

DO - 10.1007/s11128-019-2171-3

M3 - Article

VL - 18

JO - Quantum Information Processing

JF - Quantum Information Processing

SN - 1570-0755

IS - 3

M1 - 61

ER -