Phonon-Induced Exchange Gate Infidelities in Semiconducting Si-SiGe Spin Qubits

TL;DR

This paper analyzes how phonon interactions affect the fidelity of exchange gates in Si-SiGe spin qubits, revealing temperature-dependent error sources and potential mitigation strategies, with implications for quantum computing at millikelvin temperatures.

Contribution

It provides a detailed master equation analysis of phonon-induced errors in semiconductor spin qubits, identifying dominant error mechanisms and proposing pulse optimization for improved gate fidelity.

Findings

Error sources shift from spin perturbations to orbital coupling with temperature increase.

Pulse shape and length adjustments can significantly reduce phonon-induced errors.

Exchange gates remain feasible at 200-300 mK without phonon limitations.

Abstract

Spin-spin exchange interactions between semiconductor spin qubits allow for fast single and two-qubit gates. During exchange, coupling of the qubits to a surrounding phonon bath may cause errors in the resulting gate. Here, the fidelities of exchange operations with semiconductor double quantum dot spin qubits in a Si-SiGe heterostructure coupled to a finite temperature phonon bath are considered. By employing a master equation approach, the isolated effect of each spin-phonon coupling term may be resolved, as well as leakage errors of encoded qubit operations. As the temperature is increased, a crossover is observed from where the primary source of error is due to a phonon induced perturbation of the two electron spin states, to one where the phonon induced coupling to an excited orbital state becomes the dominant error. Additionally, it is shown that a simple trade-off in pulse shape and length can improve robustness to spin-phonon induced errors during gate operations by up to an order of magnitude. Our results suggest that for elevated temperatures within 200-300 mK, exchange gate operations are not currently limited by bulk phonons. This is consistent with recent experiments.