Quantum ballistic evolution in quantum mechanics: Application to quantum computers.

摘要: Quantum computers are important examples of processes whose evolution can be described in terms iterations single-step operators or their adjoints. Based on this, Hamiltonian with associated step T is investigated here. The main limitation this paper to which evolve quantum ballistically, i.e., motion restricted a collection nonintersecting distinct paths an arbitrary basis. goal proof theorem gives necessary and sufficient conditions that must satisfy so there exists description ballistic for the process, namely, partial isometry orthogonality preserving stable some Simple Turing machines one more than type elementary discussed. It seen nondeterministic basis set quite complex much entanglement present. also proven that, given operator deterministic machine, it decidable if preserving, possible. fails machine. open question such decision procedure machines. This problem does not occur classical mechanics. Also definition used here compared by other authors. \textcopyright{} 1996 American Physical Society.