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Finding spin glass ground states using quantum walks

Callison, A; Chancellor, N; Mintert, F; Kendon, V

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Authors

A Callison

N Chancellor

F Mintert



Abstract

Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better quantum advantage than for search. We uncover two general mechanisms that provide the quantum advantage: matching the driver Hamiltonian to the encoding in the problem Hamiltonian, and an energy redistribution principle that ensures a quantum walk will find a lower energy state in a short timescale. This makes it practical to use quantum walks for solving hard problems, and opens the door for a range of applications on suitable quantum hardware.

Citation

Callison, A., Chancellor, N., Mintert, F., & Kendon, V. (2019). Finding spin glass ground states using quantum walks. New Journal of Physics, 21, Article 123022. https://doi.org/10.1088/1367-2630/ab5ca2

Journal Article Type Article
Acceptance Date Nov 28, 2019
Online Publication Date Dec 13, 2019
Publication Date Dec 31, 2019
Deposit Date Dec 5, 2019
Publicly Available Date Dec 11, 2019
Journal New Journal of Physics
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 21
Article Number 123022
DOI https://doi.org/10.1088/1367-2630/ab5ca2
Related Public URLs https://arxiv.org/pdf/1903.05003

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.





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