Practical designs for permutation-symmetric problem Hamiltonians on hypercubes

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

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