Decoherence Bounds on Quantum Computation with Trapped Ions

Using simple physical arguments we investigate the capabilities of a quantum computer based on cold trapped ions. From the limitations imposed on such a device by spontaneous decay, laser phase coherence, ion heating and other sources of error, we derive a bound between the number of laser interactions and the number of ions that may be used. The largest number which may be factored using a variety of species of ion is determined.Comment: 5 pages in RevTex, 2 figures, the paper is also avalaible at http://qso.lanl.gov/qc

The Los Alamos Trapped Ion Quantum Computer Experiment

The development and theory of an experiment to investigate quantum computation with trapped calcium ions is described. The ion trap, laser and ion requirements are determined, and the parameters required for quantum logic operations as well as simple quantum factoring are described.Comment: 41 pages, 16 figures, submitted to Fortschritte der Physi

Quantum dynamics of cold trapped ions, with application to quantum computation

The theory of interactions between lasers and cold trapped ions as it pertains to the design of Cirac-Zoller quantum computers is discussed. The mean positions of the trapped ions, the eigenvalues and eigenmodes of the ions' oscillations, the magnitude of the Rabi frequencies for both allowed and forbidden internal transitions of the ions and the validity criterion for the required Hamiltonian are calculated. Energy level data for a variety of ion species is also presented.Comment: 20 pages, 7 figures, 3 table

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

Quantum computation with phase drift errors

We present results of numerical simulations of the evolution of an ion trap quantum computer made out of 18 ions which are subject to a sequence of nearly 15000 laser pulses in order to find the prime factors of N=15. We analyze the effect of random and systematic phase drift errors arising from inaccuracies in the laser pulses which induce over (under) rotation of the quantum state. Simple analytic estimates of the tolerance for the quality of driving pulses are presented. We examine the use of watchdog stabilization to partially correct phase drift errors concluding that, in the regime investigated, it is rather inefficient.Comment: 5 pages, RevTex, 2 figure