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We consider the problem of searching a d-dimensional lattice of N sites for asingle marked location. We present a Hamiltonian that solves this problem intime of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the criticaldimension d=2. This improves upon the performance of our previous quantum walksearch algorithm (which has a critical dimension of d=4), and matches theperformance of a corresponding discrete-time quantum walk algorithm. Theimprovement uses a lattice version of the Dirac Hamiltonian, and thus requiresthe introduction of spin (or coin) degrees of freedom.Comment: 5 pages, 1 figur

Spatial search and the Dirac equation