Gate Set Tomography for Spin Qubits Encoded in a Decoherence-Free Subsystem

Gate Set Tomography (GST) [1] promises to reveal coherent and incoherent errors in an assumed Markovian process model for an arbitrary set of quantum gates as well as state preparation and measurement procedures. In the form presented via the open source package pyGSTi [2], GST has had multiple successes diagnosing a variety of error sources for single and two-qubit systems. However, for qubits encoded in a decoherence-free subsystem (DFS), complications arise due to leakage, DFS gauge-freedom, and the common but ever-conflating concern of non-Markovian error processes. Here, we show the successes and failures of GST to diagnose errors for a DFS qubit composed of three electron spins in a Si/SiGe triple quantum dot, implemented in the SLEDGE platform [3]. We validate realistic simulations of 1/f noise in our triple dot system by comparing to a variety of experiments including randomized benchmarking, and then evaluate GST’s ability to evaluate error sources and leakage in the same system. It remains an ongoing open research question as to whether GST can confidently identify error types for this encoded subsystem.

[1] R. Blume-Kohout et al., Nature Communications 8, 14485 (2017)

[2] http://www.pygsti.info

[3] Ha et al., Nano Letters 22, 1443 (2022)