Practical designs for permutation-symmetric problem Hamiltonians on hypercubes

Dodds, A. Ben and Kendon, Viv and Adams, Charles S. and Chancellor, Nicholas (2019) Practical designs for permutation-symmetric problem Hamiltonians on hypercubes. Physical Review A, 100 (3). 032320. ISSN 2469-9926 (https://doi.org/10.1103/PhysRevA.100.032320)

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Abstract

We present a method to experimentally realize large-scale permutation-symmetric Hamiltonians for continuous-time quantum protocols such as quantum walks and adiabatic quantum computation. In particular, the method can be used to perform an encoded continuous-time quantum search on a hypercube graph with 2n vertices encoded into 2n qubits. We provide details for a realistically achievable implementation in Rydberg atomic systems. Although the method is perturbative, the realization is always achieved at second order in perturbation theory, regardless of the size of the mapped system. This highly efficient mapping provides a natural set of problems which are tractable both numerically and analytically, thereby providing a powerful tool for benchmarking quantum hardware and experimentally investigating the physics of continuous-time quantum protocols.

  • Item type:Article
    ID code:78858
    Dates:
    Date
    Event
    16 September 2019
    Published
    12 January 2019
    Accepted
    Notes:Reprinted with permission from the American Physical Society: Dodds, A. Ben, Kendon, Viv, Adams, Charles S. & Chancellor, Nicholas (2019). Practical designs for permutation-symmetric problem Hamiltonians on hypercubes. Physical Review A 100(3): 032320 © 2019 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
    Subjects:Science > Physics
    Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:09 Dec 2021 15:26
    Last modified:11 Apr 2024 02:21
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/78858
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