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Bounding Run-Times of Local Adiabatic Algorithms

Rao, MV Panduranga (2007) Bounding Run-Times of Local Adiabatic Algorithms. In: 4th International Conference on Theory and Applications of Models of Computation, MAY 22-25, 2007, Shanghai.

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A common trick for designing faster quantum adiabatic algorithms is to apply the adiabaticity condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigenvalues, which is an essential ingredient in the adiabaticity condition. In this paper we present a simple linear algebraic technique for obtaining a lower bound on the instantaneous gap even in such a situation. As an illustration, we investigate the adiabatic un-ordered search of van Dam et al. [17] and Roland and Cerf [15] when the non-zero entries of the diagonal final Hamiltonian are perturbed by a polynomial (in log N, where N is the length of the unordered list) amount. We use our technique to derive a bound on the running time of a local adiabatic schedule in terms of the minimum gap between the lowest two eigenvalues.

Item Type: Conference Paper
Publisher: Springer
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 11 Mar 2010 11:04
Last Modified: 19 Sep 2010 05:56
URI: http://eprints.iisc.ac.in/id/eprint/26119

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