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arXiv · 1311.7073

Improved Bounds for Eigenpath Traversal

Hao-Tien Chiang·Guanglei Xu·Rolando D. Somma
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Abstract

We present a bound on the length of the path defined by the ground states of a continuous family of Hamiltonians in terms of the spectral gap G. We use this bound to obtain a significant improvement over the cost of recently proposed methods for quantum adiabatic state transformations and eigenpath traversal. In particular, we prove that a method based on evolution randomization, which is a simple extension of adiabatic quantum computation, has an average cost of order 1/G^2, and a method based on fixed-point search, has a maximum cost of order 1/G^(3/2). Additionally, if the Hamiltonians satisfy a frustration-free property, such costs can be further improved to order 1/G^(3/2) and 1/G, respectively. Our methods offer an important advantage over adiabatic quantum computation when the gap is small, where the cost is of order 1/G^3.

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Hao-Tien Chiang, Guanglei Xu, Rolando D. Somma. 2013-11-27. Improved Bounds for Eigenpath Traversal. https://doi.org/10.1103/physreva.89.012314

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