Dalzell, A.M., Pancotti, N., Campbell, E.T. et al. (1 more author) (2023) Mind the gap: achieving a super-Grover quantum speedup by jumping to the end. In: Saha, S. and Servedio, R.A., (eds.) Proceedings of the 55th Annual ACM Symposium on Theory of Computing. STOC '23: 55th Annual ACM Symposium on Theory of Computing, 20-23 Jun 2023, Orlando, Florida. ACM , pp. 1131-1144. ISBN 9781450399135
Abstract
We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses (p-spin model), and k-local constraint satisfaction problems (k-CSP). We show that either (a) the algorithm finds the optimal solution in time O∗(2(0.5-c)n) for an n-independent constant c, a 2cn advantage over Grover's algorithm; or (b) there are sufficiently many low-cost solutions such that classical random guessing produces a (1-•) approximation to the optimal cost value in sub-exponential time for arbitrarily small choice of-•. Additionally, we show that for a large fraction of random instances from the k-spin model and for any fully satisfiable or slightly frustrated k-CSP formula, statement (a) is the case. The algorithm and its analysis are largely inspired by Hastings' short-path algorithm.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2023 ACM |
Keywords: | quantum optimization; super-Grover speedup; quantum algorithms |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 20 Jul 2023 09:09 |
Last Modified: | 20 Jul 2023 09:28 |
Status: | Published |
Publisher: | ACM |
Refereed: | Yes |
Identification Number: | 10.1145/3564246.3585203 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:201725 |