Decoherence of electron spin qubits in Si-based quantum computers

TL;DR

This paper investigates phonon-induced spin relaxation in silicon-based electron spin qubits, showing how strain and material composition influence decoherence rates, and assessing implications for quantum computer design.

Contribution

It provides a detailed analysis of phonon spin-lattice relaxation rates in Si-based qubits, highlighting the effects of strain and germanium content on decoherence.

Findings

Uniaxial compressive strain reduces relaxation rates.

High germanium content increases relaxation rates.

SiGe qubits can be optimized to minimize decoherence.

Abstract

Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate $1/T_1$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.