Controlled-NOT gate with weakly coupled qubits: Dependence of fidelity on the form of interaction

TL;DR

This paper investigates how the fidelity of a CNOT gate in weakly coupled qubits depends on the form of qubit-qubit interaction, finding that for most interactions, fidelity behavior is similar, with specific analysis for various models.

Contribution

It provides a detailed analysis of fidelity dependence on interaction form for weakly coupled qubits, including calculations for different interaction models and criteria for applicability.

Findings

Fidelity curves are largely independent of interaction form outside the Ising model.

Interaction-averaged fidelity curves are calculated for non-Ising interactions.

A criterion for when fidelity dependence on interaction form is negligible is proposed.

Abstract

An approach to the construction of the CNOT quantum logic gate for a 4-dimensional coupled-qubit model with weak but otherwise arbitrary coupling has been given recently [M. R. Geller et al., Phys. Rev. A, 012320 (2010)]. How does the resulting fidelity depend on the form of qubit-qubit coupling? In this paper we calculate intrinsic fidelity curves (fidelity in the absence of decoherence versus total gate time) for a variety of qubit-qubit interactions, including the commonly occurring isotropic Heisenberg and XY models, as well as randomly generated ones. For interactions not too close to that of the Ising model, we find that the fidelity curves do not significantly depend on the form of the interaction, and we calculate the resulting interaction-averaged fidelity curve for the non-Ising-like cases and a criterion for determining its applicability.