Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates

TL;DR

This paper investigates how spin-orbit coupling and pulse symmetry affect the fidelity of quantum gates in double quantum dot systems, revealing that deviations are proportional to spin-orbit strength and pulse asymmetry.

Contribution

It provides a detailed analysis of the impact of spin-orbit coupling and pulse symmetry on quantum gate implementation in quantum dots, including numerical simulations.

Findings

Deviations from ideal gates are proportional to spin-orbit coupling strength.

Time asymmetry in pulses worsens gate fidelity.

Time-symmetric pulses enable simple CNOT construction.

Abstract

We study the effect of spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spin-orbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the four-dimensional Hilbert space of two qubits. If the precession axis is fixed, time-symmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from time-symmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schr\"odinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spin-orbit coupling and time asymmetry of the pulse.