RESUMO
We study the standard generic quantum computer model, which describes a realistic isolated quantum computer with fluctuations in individual qubit energies and residual short-range interqubit couplings. It is shown that in the limit where the fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure, and a renormalized Hamiltonian is obtained which describes the eigenstate properties inside one band. Studies are concentrated on the central band of the computer ("core") with the highest density of states. We show that above a critical interqubit coupling strength, quantum chaos sets in, leading to a quantum ergodicity of the computer eigenstates. In this regime the ideal qubit structure disappears, the eigenstates become complex, and the operability of the computer is quickly destroyed. We confirm that the quantum chaos border decreases only linearly with the number of qubits n, although the spacing between multiqubit states drops exponentially with n. The investigation of time evolution in the quantum computer shows that in the quantum chaos regime, an ideal (noninteracting) state quickly disappears, and exponentially many states become mixed after a short chaotic time scale for which the dependence on system parameters is determined. Below the quantum chaos border an ideal state can survive for long times, and an be used for computation. The results show that a broad parameter region does exist where the efficient operation of a quantum computer is possible.
RESUMO
We study a generic model of quantum computer, composed of many qubits coupled by short-range interaction. Above a critical interqubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In this regime the noninteracting qubit structure disappears, the eigenstates become complex, and the operability of the computer is destroyed. Despite the fact that the spacing between multiqubit states drops exponentially with the number of qubits n, we show that the quantum chaos border decreases only linearly with n. This opens a broad parameter region where the efficient operation of a quantum computer remains possible.
RESUMO
We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field, both in classical and in quantum mechanics. The quantum survival probability follows the classical one up to the Heisenberg time and then decays algebraically as P(t) approximately 1/t. This decay law derives from the exponentially long times required to escape from some region of the phase space, due to tunneling and localization effects. We also provide parameter values which should allow one to observe such decay in laboratory experiments.
