Quantum computation and quantum information
Quantum computation and quantum information
A Decision Procedure for Unitary Linear Quantum Cellular Automata
SIAM Journal on Computing
On one-dimensional quantum cellular automata
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Unitarity plus causality implies localizability
Journal of Computer and System Sciences
Intrinsically universal n-dimensional quantum cellular automata
Journal of Computer and System Sciences
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We describe a model for the interaction of the internal (spin) degree of freedom of a quantum lattice-gas particle with an environmental bath. We impose the constraints that the particle-bath interaction be fixed, while the state of the bath is random, and that the effect of the particle-bath interaction be parity invariant. The condition of parity invariance defines a subgroup of the unitary group of actions on the spin degree of freedom and the bath. We derive a general constraint on the Lie algebra of the unitary group which defines this subgroup, and hence guarantees parity invariance of the particle-bath interaction. We show that generalizing the quantum lattice gas in this way produces a model having both classical and quantum discrete random walks as different limits. We present preliminary simulation results illustrating the intermediate behavior in the presence of weak quantum noise