Optimization of a solid-state electron spin qubit using Gate Set Tomography

TL;DR

This paper demonstrates the use of Gate Set Tomography to precisely characterize and improve the fidelity of a solid-state electron spin qubit, revealing systematic errors and non-Markovian noise.

Contribution

The study applies GST to a high-fidelity electron spin qubit, achieving a new fidelity benchmark and identifying error sources that improve calibration and understanding.

Findings

Achieved a gate fidelity of 99.942(8)% after calibration.

GST revealed systematic calibration errors not detected by randomized benchmarking.

Identified high levels of non-Markovian noise affecting qubit performance.

Abstract

State of the art qubit systems are reaching the gate fidelities required for scalable quantum computation architectures. Further improvements in the fidelity of quantum gates demands characterization and benchmarking protocols that are efficient, reliable and extremely accurate. Ideally, a benchmarking protocol should also provide information on how to rectify residual errors. Gate Set Tomography (GST) is one such protocol designed to give detailed characterization of as-built qubits. We implemented GST on a high-fidelity electron-spin qubit confined by a single $^{31}$P atom in $^{28}$Si. The results reveal systematic errors that a randomized benchmarking analysis could measure but not identify, whereas GST indicated the need for improved calibration of the length of the control pulses. After introducing this modification, we measured a new benchmark average gate fidelity of $99.942(8)\%$, an improvement on the previous value of $99.90(2)\%$. Furthermore, GST revealed high levels of non-Markovian noise in the system, which will need to be understood and addressed when the qubit is used within a fault-tolerant quantum computation scheme.