Thermal noise in a solid state quantum computer

Abstract

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.