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Quantum search with hybrid adiabatic–quantum-walk algorithms and realistic noise

Morley, James G.; Chancellor, Nicholas; Bose, Sougato; Kendon, Viv

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Authors

James G. Morley

Nicholas Chancellor

Sougato Bose



Abstract

Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near term. Adiabatic quantum computing, quantum annealing, computation by a continuous-time quantum walk, and special purpose quantum simulators all use this strategy. In this work, we carry out a detailed examination of adiabatic and quantum-walk implementation of the quantum search algorithm, using the more physically realistic hypercube connectivity, rather than the complete graph, for our base Hamiltonian. We calculate optimal adiabatic schedules both analytically and numerically for the hypercube and then interpolate between adiabatic and quantum-walk searching, obtaining a family of hybrid algorithms. We show that all of these hybrid algorithms provide the quadratic quantum speedup when run with optimal parameter settings, which we determine and discuss in detail. We incorporate the effects of multiple runs of the same algorithm, noise applied to the qubits, and two types of problem misspecification, determining the optimal hybrid algorithm for each case. Our results reveal a rich structure of how these different computational mechanisms operate and should be balanced in different scenarios. For large systems with low noise and good control, a quantum walk is the best choice, while hybrid strategies can mitigate the effects of many shortcomings in hardware and problem misspecification.

Citation

Morley, J. G., Chancellor, N., Bose, S., & Kendon, V. (2019). Quantum search with hybrid adiabatic–quantum-walk algorithms and realistic noise. Physical Review A, 99(2), Article 022339. https://doi.org/10.1103/physreva.99.022339

Journal Article Type Article
Acceptance Date Jan 3, 2019
Online Publication Date Feb 28, 2019
Publication Date Feb 28, 2019
Deposit Date Mar 5, 2019
Publicly Available Date Mar 29, 2024
Journal Physical Review A
Print ISSN 2469-9926
Electronic ISSN 2469-9934
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 99
Issue 2
Article Number 022339
DOI https://doi.org/10.1103/physreva.99.022339

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

Copyright Statement
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.




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