Adiabatic Quantum Computing for Random Satisfiability Problems

Details Adiabatic Quantum Computing for Random Satisfiability Problems Adiabatic Quantum Computing for Random Satisfiability Problems

2002-06-11

arxiv.org/abs/quant-ph/0206059v2

Phys Rev A 67 022314 (2003)

Physics

Quantum Physics

added discussion of discrete adiabatic method, and simulations with 30 bits 8 pages, 8 figures

Scientific paper

10.1103/PhysRevA.67.022314

The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables, the adiabatic method gives solution probabilities close to 1 for problem sizes feasible to evaluate via simulation on current computers. However, for these sizes the minimum energy gaps of most instances are fairly large, so the good performance scaling seen for small problems may not reflect asymptotic behavior where costs are dominated by tiny gaps. Moreover, the resulting search costs are much higher than for other methods. Variants of the quantum algorithm that do not match the adiabatic limit give lower costs, on average, and slower growth than the conventional GSAT heuristic method.

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