@article {1213,
title = {Spatial search and the Dirac equation},
journal = {Physical Review A},
volume = {70},
year = {2004},
month = {2004/10/19},
abstract = { 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.
},
doi = {10.1103/PhysRevA.70.042312},
url = {http://arxiv.org/abs/quant-ph/0405120v1},
author = {Andrew M. Childs and Jeffrey Goldstone}
}