Quantum lattice-gas model for the many-particle Schr{umlt o}dinger equation in d dimensions
- Center for Computational Science, Boston University, 3 Cummington Street, Boston, Massachusetts 02215 (United States)
- Department of Physics, Princeton University, Princeton, New Jersey 08544 (United States)
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 Schr{umlt o}dinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schr{umlt o}dinger 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. {copyright} {ital 1998} {ital The American Physical Society}
- OSTI ID:
- 567019
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 1 Vol. 57; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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