1996/04/29 by Bruce M. Boghosian, Boghosian, Bruce M., Washington Taylor +1
Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Quantum Physics (quant-ph) #comp-gas #hep-lat #nlin.CG #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9604035
19 pages LaTeX, one illustration
arxiv created 1997/01/16 · arxiv updated 2009/11/30
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schroedinger 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.