Quantum Adiabatic Algorithms, Small Gaps, and Different Paths
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Farhi_Quantum adiabatic.pdf
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Author(s)
Farhi, Edward
Goldstone, Jeffrey
Gosset, David Nicholas
Gutmann, Sam
Meyer, Harvey B.
Shor, Peter W.
Date Issued
March 2011
Journal
Quantum Information & Computation
Publisher
Rinton Press
Citation
Edward Farhi, Jeffrey Goldston, David Gosset, Sam Gutmann, Harvey B. Meyer, and Peter Shor. 2011. Quantum adiabatic algorithms, small gaps, and different paths. Quantum Info. Comput. 11, 3 (March 2011), 181-214.
Version
Original manuscript
Abstract
We construct a set of instances of 3SAT which are not solved efficiently using the simplestquantum adiabatic algorithm. These instances are obtained by picking randomclauses all consistent with two disparate planted solutions and then penalizing one ofthem with a single additional clause. We argue that by randomly modifying the beginningHamiltonian, one obtains (with substantial probability) an adiabatic path thatremoves this difficulty. This suggests that the quantum adiabatic algorithm should ingeneral be run on each instance with many different random paths leading to the problemHamiltonian. We do not know whether this trick will help for a random instance of3SAT (as opposed to an instance from the particular set we consider), especially if theinstance has an exponential number of disparate assignments that violate few clauses.We use a continuous imaginary time Quantum Monte Carlo algorithm in a novel way tonumerically investigate the ground state as well as the first excited state of our system.Our arguments are supplemented by Quantum Monte Carlo data from simulations withup to 150 spins.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
http://dl.acm.org/citation.cfm?id=2011396
