24,948 research outputs found
Quantum computing classical physics
In the past decade quantum algorithms have been found which outperform the
best classical solutions known for certain classical problems as well as the
best classical methods known for simulation of certain quantum systems. This
suggests that they may also speed up the simulation of some classical systems.
I describe one class of discrete quantum algorithms which do so--quantum
lattice gas automata--and show how to implement them efficiently on standard
quantum computers.Comment: 13 pages, plain TeX, 10 PostScript figures included with epsf.tex;
for related work see http://math.ucsd.edu/~dmeyer/research.htm
Quantum games and quantum algorithms
A quantum algorithm for an oracle problem can be understood as a quantum
strategy for a player in a two-player zero-sum game in which the other player
is constrained to play classically. I formalize this correspondence and give
examples of games (and hence oracle problems) for which the quantum player can
do better than would be possible classically. The most remarkable example is
the Bernstein-Vazirani quantum search algorithm which I show creates no
entanglement at any timestep.Comment: 10 pages, plain TeX; to appear in the AMS Contemporary Mathematics
volume: Quantum Computation and Quantum Information Science; revised remarks
about other quantum games formalisms; for related work see
http://math.ucsd.edu/~dmeyer/research.htm
Quantum mechanics of lattice gas automata. II. Boundary conditions and other inhomogeneities
We continue our analysis of the physics of quantum lattice gas automata
(QLGA). Previous work has been restricted to periodic or infinite lattices;
simulation of more realistic physical situations requires finite sizes and
non-periodic boundary conditions. Furthermore, envisioning a QLGA as a
nanoscale computer architecture motivates consideration of inhomogeneities in
the `substrate'; this translates into inhomogeneities in the local evolution
rules. Concentrating on the one particle sector of the model, we determine the
various boundary conditions and rule inhomogeneities which are consistent with
unitary global evolution. We analyze the reflection of plane waves from
boundaries, simulate wave packet refraction across inhomogeneities, and
conclude by discussing the extension of these results to multiple particles.Comment: 24 pages, plain TeX, 9 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages), 3 additional large figures
available upon request or from
http://math.ucsd.edu/~dmeyer/papers/papers.htm
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