From Gauge Transformations to Topology Computation in Quantum Lattice Gas Automata
نویسنده
چکیده
The evolution of a quantum lattice gas automaton (LGA) for a single charged particle is invariant under multiplication of the wave function by a global phase. Requiring invariance under the corresponding local gauge transformations determines the rule for minimal coupling to an arbitrary external electromagnetic field. We develop the Aharonov-Bohm effect in the resulting model into a constant time algorithm to distinguish a one dimensional periodic lattice from one with boundaries; any classical deterministic LGA algorithm distinguishing these two spatial topologies would have expected running time on the order of the cardinality of the lattice. PACS numbers: 03.65.Lx, 03.65.Vf, 03.65.Pm.
منابع مشابه
Quantum Mechanics of Lattice Gas Automata I. One Particle Plane Waves and Potentials
Classical lattice gas automata effectively simulate physical processes such as diffusion and fluid flow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Stud...
متن کاملQuantum Mechanics of Lattice Gas Automatai . One Particle Plane
Classical lattice gas automata eeectively simulate physical processes such as diiusion and uid ow (in certain parameter regimes) despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently deened quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can eeectively simulate. Studying the...
متن کاملFUZZY PREORDERED SET, FUZZY TOPOLOGY AND FUZZY AUTOMATON BASED ON GENERALIZED RESIDUATED LATTICE
This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.
متن کاملLattice Gas Automata Simulation of Adsorption Process of Polymer in Porous Media
Lattice gas automata (LGA) model is developed to simulate polymer adsorption process by adding some collision rules. The simulation result of the model is matched with batch experiment and compared with accepted isothermal adsorption equations. They show that the model is viable to perform simulation of the polymer adsorption process. The LGA model is then applied for simulating continuous poly...
متن کاملFrom Quantum Cellular Automata to Quantum Lattice Gases
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial...
متن کامل