Spatial search and the Dirac equation
量子物理
2007-05-23 v1
摘要
We consider the problem of searching a d-dimensional lattice of N sites for a single marked location. We present a Hamiltonian that solves this problem in time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical dimension d=2. This improves upon the performance of our previous quantum walk search algorithm (which has a critical dimension of d=4), and matches the performance of a corresponding discrete-time quantum walk algorithm. The improvement uses a lattice version of the Dirac Hamiltonian, and thus requires the introduction of spin (or coin) degrees of freedom.
引用
@article{arxiv.quant-ph/0405120,
title = {Spatial search and the Dirac equation},
author = {Andrew M. Childs and Jeffrey Goldstone},
journal= {arXiv preprint arXiv:quant-ph/0405120},
year = {2007}
}
备注
5 pages, 1 figure