%0 Journal Article %J Physical Review A %D 2004 %T Spatial search and the Dirac equation %A Andrew M. Childs %A Jeffrey Goldstone %X 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. %B Physical Review A %V 70 %8 2004/10/19 %G eng %U http://arxiv.org/abs/quant-ph/0405120v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.70.042312