Classical and quantum annealing in the median of three-satisfiability

Neuhaus, T.; Peschina, M.; De Raedt, H.; Michielsen, K.

doi:10.1103/PhysRevA.83.012309

Journal Article

PreJuSER-14076

Classical and quantum annealing in the median of three-satisfiability

Neuhaus, T.FZJ* ; Peschina, M.FZJ* ; Michielsen, K.FZJ* ; De Raedt, H.

2011
APS College Park, Md.

Physical review / A 83(1), 012309 (2011) [10.1103/PhysRevA.83.012309]

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Please use a persistent id in citations: http://hdl.handle.net/2128/11169 doi:10.1103/PhysRevA.83.012309

Abstract: We determine the classical and quantum complexities of a specific ensemble of three-satisfiability problems with a unique satisfying assignment for up to N = 100 and 80 variables, respectively. In the classical limit, we employ generalized ensemble techniques and measure the time that a Markovian Monte Carlo process spends in searching classical ground states. In the quantum limit, we determine the maximum finite correlation length along a quantum adiabatic trajectory determined by the linear sweep of the adiabatic control parameter in the Hamiltonian composed of the problem Hamiltonian and the constant transverse field Hamiltonian. In the median of our ensemble, both complexities diverge exponentially with the number of variables. Hence, standard, conventional adiabatic quantum computation fails to reduce the computational complexity to polynomial. Moreover, the growth-rate constant in the quantum limit is 3.8 times as large as the one in the classical limit, making classical fluctuations more beneficial than quantum fluctuations in ground-state searches.

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Note: T.N. thanks the Theory Department at Bielefeld University for extended hospitality. Calculations were performed on the JUMP and JUROPA supercomputers at JSC and on the NICOLE workstation cluster of NIC (VSR Grant No. JJSC02). This work is partially supported by NCF, the Netherlands.

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