  We construct a quantum random walk algorithm, based on the Dirac operator
instead of the Laplacian. The algorithm explores multiple evolutionary branches
by superposition of states, and does not require the coin toss instruction of
classical randomised algorithms. We use this algorithm to search for a marked
vertex on a hypercubic lattice in arbitrary dimensions. Our numerical and
analytical results match the scaling behaviour of earlier algorithms that use a
coin toss instruction.
