Campbell, E., Khurana, A. and Montanaro, A. (2019) Applying quantum algorithms to constraint satisfaction problems. Quantum, 3. 167. ISSN 2521-327X
Abstract
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best classical algorithms and taking into account realistic hardware parameters and overheads for fault-tolerance. All known examples of such speedups correspond to problems related to simulation of quantum systems and cryptography. Here we apply general-purpose quantum algorithms for solving constraint satisfaction problems to two families of prototypical NP-complete problems: boolean satisfiability and graph colouring. We consider two quantum approaches: Grover's algorithm and a quantum algorithm for accelerating backtracking algorithms. We compare the performance of optimised versions of these algorithms, when applied to random problem instances, against leading classical algorithms. Even when considering only problem instances that can be solved within one day, we find that there are potentially large quantum speedups available. In the most optimistic parameter regime we consider, this could be a factor of over 10^5 relative to a classical desktop computer; in the least optimistic regime, the speedup is reduced to a factor of over 10^3. However, the number of physical qubits used is extremely large, and improved fault-tolerance methods will likely be needed to make these results practical. In particular, the quantum advantage disappears if one includes the cost of the classical processing power required to perform decoding of the surface code using current techniques.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Authors. |
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) |
Funding Information: | Funder Grant number Engineering and Physical Science Research Council (EPSRC) EP/M024261/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 Jul 2019 10:19 |
Last Modified: | 30 Jul 2019 10:19 |
Status: | Published |
Publisher: | Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften |
Refereed: | Yes |
Identification Number: | 10.22331/q-2019-07-18-167 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:148990 |