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Practical designs for permutation-symmetric problem Hamiltonians on hypercubes

Dodds, A. Ben; Kendon, Viv; Adams, Charles S.; Chancellor, Nicholas

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Authors

A. Ben Dodds



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.

Citation

Dodds, A. B., Kendon, V., Adams, C. S., & Chancellor, N. (2019). Practical designs for permutation-symmetric problem Hamiltonians on hypercubes. Physical Review A, 100(3), Article 032320. https://doi.org/10.1103/physreva.100.032320

Journal Article Type Article
Online Publication Date Sep 16, 2019
Publication Date Sep 30, 2019
Deposit Date Oct 8, 2019
Publicly Available Date Oct 8, 2019
Journal Physical Review A
Print ISSN 2469-9926
Electronic ISSN 2469-9934
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 100
Issue 3
Article Number 032320
DOI https://doi.org/10.1103/physreva.100.032320
Public URL https://durham-repository.worktribe.com/output/1289189
Related Public URLs https://arxiv.org/abs/1812.07885

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Copyright Statement
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.






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