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(Sub)Exponential advantage of adiabatic Quantum computation with no sign problem

Authors:

András Gilyén,

Matthew B. Hastings,

Umesh VaziraniAuthors Info & Claims

STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

Pages 1357 - 1369

https://doi.org/10.1145/3406325.3451060

Published: 15 June 2021 Publication History

Abstract

We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. The Hamiltonian that exhibits this speed-up comes from the adjacency matrix of an undirected graph whose vertices are labeled by n-bit strings, and we can view the adiabatic evolution as an efficient O(poly(n))-time quantum algorithm for finding a specific “EXIT” vertex in the graph given the “ENTRANCE” vertex. On the other hand we show that if the graph is given via an adjacency-list oracle, there is no classical algorithm that finds the “EXIT” with probability greater than exp(−n^δ) using at most exp(n^δ) queries for δ= 1/5 − o(1). Our construction of the graph is somewhat similar to the “welded-trees” construction of Childs et al., but uses additional ideas of Hastings for achieving a spectral gap and a short adiabatic path.

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Cited By

Gharibian S(2024)Guest Column: The 7 faces of quantum NPACM SIGACT News10.1145/3639528.363953554:4(54-91)Online publication date: 3-Jan-2024
https://dl.acm.org/doi/10.1145/3639528.3639535
Ben-David SChilds AGilyén AKretschmer WPodder SWang D(2024)Symmetries, Graph Properties, and Quantum SpeedupsSIAM Journal on Computing10.1137/23M157397553:6(FOCS20-368-FOCS20-415)Online publication date: 13-Dec-2024
https://doi.org/10.1137/23M1573975
Chowdhury SCamsari KDatta S(2023)Accelerated quantum Monte Carlo with probabilistic computersCommunications Physics10.1038/s42005-023-01202-36:1Online publication date: 27-Apr-2023
https://doi.org/10.1038/s42005-023-01202-3
Show More Cited By

Index Terms

(Sub)Exponential advantage of adiabatic Quantum computation with no sign problem
1. Theory of computation
  1. Models of computation
    1. Quantum computation theory
      1. Quantum complexity theory

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cover image ACM Conferences

STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

June 2021

1797 pages

ISBN:9781450380539

DOI:10.1145/3406325

General Chair:
Samir Khuller
Northwestern University, USA
,
Program Chair:
Virginia Vassilevska Williams
Massachusetts Institute of Technology, USA

Copyright © 2021 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 June 2021

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Simons Institute for the Theory of Computing
NSF (National Science Foundation)
Vannevar Bush faculty fellowship
Samsung

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STOC '21

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SIGACT

STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing

June 21 - 25, 2021

Virtual, Italy

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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57th Annual ACM Symposium on Theory of Computing (STOC 2025)

June 23 - 27, 2025

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Citations

Cited By

Gharibian S(2024)Guest Column: The 7 faces of quantum NPACM SIGACT News10.1145/3639528.363953554:4(54-91)Online publication date: 3-Jan-2024
https://dl.acm.org/doi/10.1145/3639528.3639535
Ben-David SChilds AGilyén AKretschmer WPodder SWang D(2024)Symmetries, Graph Properties, and Quantum SpeedupsSIAM Journal on Computing10.1137/23M157397553:6(FOCS20-368-FOCS20-415)Online publication date: 13-Dec-2024
https://doi.org/10.1137/23M1573975
Chowdhury SCamsari KDatta S(2023)Accelerated quantum Monte Carlo with probabilistic computersCommunications Physics10.1038/s42005-023-01202-36:1Online publication date: 27-Apr-2023
https://doi.org/10.1038/s42005-023-01202-3
Kantabutra S(2023)Adiabatic Quantum Computation for Cyber Attack and Defense StrategiesNew Trends in Computer Technologies and Applications10.1007/978-981-19-9582-8_9(98-110)Online publication date: 10-Feb-2023
https://doi.org/10.1007/978-981-19-9582-8_9
Moosavian AKahani SBeigi S(2022)Limits of Short-Time Evolution of Local HamiltoniansQuantum10.22331/q-2022-06-27-7446(744)Online publication date: 27-Jun-2022
https://doi.org/10.22331/q-2022-06-27-744
Crosson ELidar D(2021)Prospects for quantum enhancement with diabatic quantum annealingNature Reviews Physics10.1038/s42254-021-00313-63:7(466-489)Online publication date: 28-May-2021
https://doi.org/10.1038/s42254-021-00313-6

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