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Kluwer Academic Publishers eBooks

Decoherence and Fidelity of Single Qubit Operations in a Solid State Quantum Computer

Cameron J. Wellard, Lloyd C. L. Hollenberg

Published Feb 24, 2006• 0 citations
Publisher

Abstract

We examine a stochastic noise process that causes phase damping of qubits in the quantum register of the solid state quantum computer proposed by Kane
DOI
10.1007/0-306-47114-0_40

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The method of iterated resolvents is used to obtain an effective Hamiltonian for neighboring qubits in the Kane solid-state quantum computer. In contrast to the adiabatic gate processes inherent in the Kane proposal we show that free evolution of the qubit-qubit system, as generated by this effective Hamiltonian, combined with single-qubit operations, is sufficient to produce a controlled-NOT gate. Thus the usual set of universal gates can be obtained on the Kane quantum computer without the need for adiabatic switching of the controllable parameters as prescribed by Kane [Nature (London) 393, 133 (1998)]. Both the fidelity and the gate time of this nonadiabatic controlled-NOT gate are determined by numerical simulation.
The Kane proposal for the construction of a solid state quantum computer calls for the placement of a metallic A-gate above each nuclear qubit. Voltage biases applied to these A-gates are to be used to control the evolution of the qubits. In this paper, we consider the decohering effect of thermal fluctuations, the so-called Johnson noise, in the A-gate biases, on the average evolution of qubits undergoing single qubit rotations, as well as those that are not undergoing any operation at all. We find that although the errors introduced are of a different nature for each case, phase errors for the static qubits and both phase and bit-flip errors for qubits undergoing operations, the net error probability is similar for both, and low enough when compared to the timescale of single qubit operations for them to be corrected efficiently.
In this paper we investigate the implementation of single-qubit operations in the Kane solid-state quantum computer by Rabi flipping the nuclear qubits via the application of resonant radio-frequency fields. Specifically, we calculate the change in the resonance frequency of the nuclear qubits with the application of electric potentials to metallic control gates designed to address individual qubits, as well as the effects these fields have on neighbouring qubits. We find that although the resonance frequencies of the neighbouring qubits are shifted, it is still theoretically possible to implement single-qubit operations with the fidelity required for large-scale quantum computation using this technique.