Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
Name
Farhi-2012-Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs.pdf
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Author(s)
Farhi, Edward
Shor, Peter W.
Gosset, David Nicholas
Hen, Itay
Sandvik, A. W.
Young, A. P.
Zamponi, Francesco
Date Issued
November 2012
Journal
Physical Review A
Publisher
American Physical Society
Citation
Farhi, Edward et al. “Performance of the Quantum Adiabatic Algorithm on Random Instances of Two Optimization Problems on Regular Hypergraphs.” Physical Review A 86.5 (2012). © 2012 American Physical Society
Version
Final published version
Abstract
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular max-cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular max-cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.86.052334
