Quantum lattice-gas model for the many-particle Schrödinger equation in $d$ dimensions

We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wave function satisfying a Schrödinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schrödinger particle and the eigenvalues of a unitary matrix describing the local evolution of the model. Second quantized versions of these unitary models can be defined, describing in the continuum limit the evolution of a nonrelativistic quantum many-body theory. An arbitrary potential is easily incorporated into these systems. The models we describe fall in the class of quantum lattice-gas automata and can be implemented on a quantum computer with a speedup exponential in the number of particles in the system. This gives an efficient algorithm for simulating general nonrelativistic interacting quantum many-body systems on a quantum computer.