Perturbation Theory for Quantum Computation with Large Number of Qubits

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.Comment: 8 pages RevTex including 2 figure

Dynamical Stability and Quantum Chaos of Ions in a Linear Trap

The realization of a paradigm chaotic system, namely the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev

Relaxation and Zeno effect in qubit measurements

We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate.Comment: some clarifications added, to appear in Phys. Rev. Let

Non-Resonant Effects in Implementation of Quantum Shor Algorithm

We simulate Shor's algorithm on an Ising spin quantum computer. The influence of non-resonant effects is analyzed in detail. It is shown that our ``$2\pi k$''-method successfully suppresses non-resonant effects even for relatively large values of the Rabi frequency.Comment: 11 pages, 13 figure

Solid-State Nuclear Spin Quantum Computer Based on Magnetic Resonance Force Microscopy

We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that an MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids: (a) preparation of the ground state, (b) one- and two- qubit quantum logic gates, and (c) a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1K.Comment: 16 pages, 5 figure

Magnetic Field Satellite (Magsat) data processing system specifications

The software specifications for the MAGSAT data processing system (MDPS) are presented. The MDPS is divided functionally into preprocessing of primary input data, data management, chronicle processing, and postprocessing. Data organization and validity, and checks of spacecraft and instrumentation are dicussed. Output products of the MDPS, including various plots and data tapes, are described. Formats for important tapes are presented. Dicussions and mathematical formulations for coordinate transformations and field model coefficients are included

Radiative Tail in πe2\pi_{e2} Decay and Some Comments on μ−e\mu-e Universality

The result of lowest-order perturbation theory calculations of the photon and positron spectra in radiative pion(e2) decay are generalized to all orders of perturbation theory using the structure-function method. An additional source of radiative corrections to the ratio of the positron and muon channels of pion decay, due to emission of virtual and real photons and pairs, is considered. It depends on details of the detection of the final particles and is large enough to be taken into account in theoretical estimates with a level of accuracy of 0.1%.Comment: 5 pages, LaTeX, some misprints are corrected, submitted to Pisma Zh. Eksp. Teor. Fi

Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem of Electron Localization

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the cites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems.Comment: 18 pages RevTe

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 any 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 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.Comment: 9 pages, 6 figures, submitted to PR

Double-Slit Interferometry with a Bose-Einstein Condensate

A Bose-Einstein "double-slit" interferometer has been recently realized experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevski equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong dephasing observed experimentally. The role of quantum fluctuations is discussed.Comment: 4 pages, 3 figure