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State of the art qubit systems are reaching the gate fidelities required forscalable quantum computation architectures. Further improvements in thefidelity of quantum gates demands characterization and benchmarking protocolsthat are efficient, reliable and extremely accurate. Ideally, a benchmarkingprotocol should also provide information on how to rectify residual errors.Gate Set Tomography (GST) is one such protocol designed to give detailedcharacterization of as-built qubits. We implemented GST on a high-fidelityelectron-spin qubit confined by a single $^{31}$P atom in $^{28}$Si. Theresults reveal systematic errors that a randomized benchmarking analysis couldmeasure but not identify, whereas GST indicated the need for improvedcalibration of the length of the control pulses. After introducing thismodification, 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 afault-tolerant quantum computation scheme.

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