Experimental Measurement of Leakage-Error in Exchange-Only SiGe Quantum Dot Qubits by Extending Randomized Benchmarking

Randomized benchmarking is a common method for quantifying qubit gate error, but has questionable validity or reliability for some physically relevant error sources. The focus of this talk will be leakage out of the computational subspace of a decoherence-free subsystem, which can introduce additional benchmarking decay and unreliable error estimates. Though techniques have been developed to characterize leakage, it is not clear how best to use that information to inform computational error rates. Here we develop an extension to the randomized benchmarking protocol that estimates both computational and leakage errors by means of preparing and tracking different final states of the benchmarking sequence. Using this protocol, we experimentally measure the leakage error per gate in an exchange-only SiGe triple quantum dot at rates well below that of state-preparation-and-measurement (SPAM) error and pulse error from electrical noise. These leakage rates are in close agreement with a noise model with electrical and hyperfine-induced magnetic noise terms.