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\"odinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schr\"odinger 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.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\"odinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schr\"odinger 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.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJan 1, 1998101 citations

Simulating the time-dependent Schr"odinger equation with a quantum lattice-gas algorithm

Zachary Prezkuta, Mark W. Coffey

Bulletin of the American Physical SocietyMar 8, 20070 citations

Hyperspherical description of the degenerate Fermi gas: s -wave interactions

Seth T. Rittenhouse, M. J. Cavagnero, Javier von Stecher +1 more

We present a unique theoretical description of the physics of the spherically trapped $N$ -atom degenerate Fermi gas at zero temperature based on an ordinary Schr\"odinger equation with a microscopic, two-body interaction potential. With a careful choice of coordinates and a variational wave function, the many-body Schr\"odinger equation can be accurately described by a linear, one-dimensional effective Schr\"odinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius, and peak density of the ground-state energy are made to those predicted by Hartree-Fock (HF) theory. Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.We present a unique theoretical description of the physics of the spherically trapped $N$-atom degenerate Fermi gas at zero temperature based on an ordinary Schr\"odinger equation with a microscopic, two-body interaction potential. With a careful choice of coordinates and a variational wave function, the many-body Schr\"odinger equation can be accurately described by a linear, one-dimensional effective Schr\"odinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius, and peak density of the ground-state energy are made to those predicted by Hartree-Fock (HF) theory. Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.

arXiv:cond-mat/0607340Physical Review ANov 28, 200620 citations

Method for the Direct Solve of the Many-Body Schr\"{o}dinger Wave Equation

J. Jerke, C. J. Tymczak, Bill Poirier

Bulletin of the American Physical SocietyMar 13, 20170 citations

Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation

Bruce M. Boghosian, Washington Taylor

A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schrodinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schrodinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.

Jan 14, 199731 citations

We present a unique theoretical description of the physics of the spherically trapped

N

-atom degenerate Fermi gas at zero temperature based on an ordinary Schr\"odinger equation with a microscopic, two-body interaction potential. With a careful choice of coordinates and a variational wave function, the many-body Schr\"odinger equation can be accurately described by a linear, one-dimensional effective Schr\"odinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius, and peak density of the ground-state energy are made to those predicted by Hartree-Fock (HF) theory. Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.