Finding spin glass ground states using quantum walks

Callison, Adam and Chancellor, Nicholas and Mintert, Florian and Kendon, Viv (2019) Finding spin glass ground states using quantum walks. New Journal of Physics, 21. 123022. ISSN 1367-2630 (https://doi.org/10.1088/1367-2630/ab5ca2)

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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.

  • Item type:Article
    ID code:78857
    Dates:
    Date
    Event
    13 December 2019
    Published
    18 October 2019
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:09 Dec 2021 15:15
    Last modified:11 Apr 2024 02:21
    URI:https://strathprints.strath.ac.uk/id/eprint/78857
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