Statistical exchange-coupling errors and the practicality of scalable silicon donor qubits

TL;DR

This paper investigates the statistical variability of exchange coupling between donor pairs in silicon, highlighting challenges for scalable silicon-based quantum computing due to placement errors affecting qubit interactions.

Contribution

The study provides a detailed simulation of exchange coupling errors caused by donor placement straggles, offering insights into the practical limitations for silicon donor qubits.

Findings

Significant variability in exchange coupling due to placement errors.

Difficulty in achieving precise $J$ values for scalable quantum gates.

Challenges persist even with small donor separations and controlled placement.

Abstract

Recent experimental efforts have led to considerable interest in donor-based localized electron spins in Si as viable qubits for a scalable silicon quantum computer. With the use of isotopically purified $^{28}$Si and the realization of extremely long spin coherence time in single-donor electrons, the recent experimental focus is on two-coupled donors with the eventual goal of a scaled-up quantum circuit. Motivated by this development, we simulate the statistical distribution of the exchange coupling $J$ between a pair of donors under realistic donor placement straggles, and quantify the errors relative to the intended $J$ value. With $J$ values in a broad range of donor-pair separation ($5<|\mathbf{R}|<60$ nm), we work out various cases systematically, for a target donor separation $\mathbf{R}_0$ along the [001], [110] and [111] Si crystallographic directions, with $|\mathbf{R}_0|=10, 20$ or 30 nm and standard deviation $\sigma_R=1, 2, 5$ or 10 nm. Our extensive theoretical results demonstrate the great challenge for a prescribed $J$ gate even with just a donor pair, a first step for any scalable Si-donor-based quantum computer.