Dynamical fidelity of a solid-state quantum computation.

In this paper we analyze the dynamics in a spin model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows us to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.

Symmetry of quantum phase space in a degenerate Hamiltonian system.

The structure of the global "quantum phase space" is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small. Usually, the phenomenon of quantum resonance was studied in nondegenerate [G. M. Zaslavsky, Chaos in Dynamic Systems (Harwood Academic, Chur, 1985)] and degenerate [Demikhovskii, Kamenev, and Luna-Acosta, Phys. Rev. E 52, 3351 (1995)] classically chaotic systems only in the particular regions of the classical phase space, such as the center of the resonance or near the separatrix. The system under consideration is degenerate, and even an infinitely small perturbation generates in the classical phase space an infinite number of the resonant cells which are arranged in the pattern with the axial symmetry of the order 2&mgr; (where &mgr; is the resonance number). We show analytically that the Husimi functions of all Floquet states (the quantum phase space) have the same symmetry as the classical phase space. This correspondence is demonstrated numerically for the Husimi functions of the Floquet states corresponding to the motion near the elliptic stable points (centers of the classical resonance cells). The derived results are valid in the resonance approximation when the perturbation amplitude is small enough, and the stochastic layers in the classical phase space are exponentially thin. The developed approach can be used for studying a global symmetry of more complicated quantum systems with chaotic behavior. (c) 2000 American Institute of Physics.