How Powerful is Adiabatic Quantum Computation?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The quantum adiabatic optimization algorithm and local minima
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A study of heuristic guesses for adiabatic quantum computation
Quantum Information Processing
Quantum Information & Computation
Unstructured randomness, small gaps and localization
Quantum Information & Computation
Experimental evaluation of an adiabiatic quantum system for combinatorial optimization
Proceedings of the ACM International Conference on Computing Frontiers
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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.