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

Simulations of Quantum Logic Operations in Quantum Computer with Large Number of Qubits

We report the first simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain in which selective excitations of spins is provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum control-not (CN) gate implementation for remote qubits which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum logic gates involving a large number of qubits.Comment: 13 pages, 15 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

Quantum computing with magnetic atoms in optical lattices of reduced periodicity

We investigate the feasibility of combining Raman optical lattices with a quantum computing architecture based on lattice-confined magnetically interacting neutral atoms. A particular advantage of the standing Raman field lattices comes from reduced interatomic separations leading to increased interatomic interactions and improved multi-qubit gate performance. Specifically, we analyze a $J=3/2$ Zeeman system placed in $_{+}-\sigma_{-}$ Raman fields which exhibit $\lambda /4$ periodicity. We find that the resulting CNOT gate operations times are in the order of millisecond. We also investigate motional and magnetic-field induced decoherences specific to the proposed architecture

A Magnetic Resonance Force Microscopy Quantum Computer with Tellurium Donors in Silicon

We propose a magnetic resonance force microscopy (MRFM)-based nuclear spin quantum computer using tellurium impurities in silicon. This approach to quantum computing combines the well-developed silicon technology with expected advances in MRFM.Comment: 9 pages, 1 figur

Single electron capacitance spectroscopy of vertical quantum dots using a single electron transistor

We have incorporated an aluminum single electron transistor (SET) directly on top of a vertical quantum dot, enabling the use of the SET as an electrometer that is extremely responsive to the motion of charge into and out of the dot. Charge induced on the SET central island from single electron additions to the dot modulates the SET output, and we describe two methods for demodulation that permit quantitative extraction of the quantum dot capacitance signal. The two methods produce closely similar results for the determined single electron capacitance peaks.Comment: Submitted to Applied Physics Letters (reformatted to fit correctly on a page

On Berenstein-Douglas-Seiberg Duality

I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the requirements. Then I explicitly show that a pair of toric dual quivers is also dual according to their proposal. All these computations go beyond tilting modules, and really work in the derived category. I introduce all necessary mathematics where needed.Comment: 22 pages, LaTe