Magnetic gradient fluctuation compensation during universal control of a Si/SiGe exchange-only qubit

Time-fluctuating local magnetic fields are a significant noise source affecting spin qubits. In exchange-only qubits encoded in a decoherence-free subsystem (DFS), magnetic field gradients cause both error and leakage out of the encoding [1]. For quantum dots in Si/SiGe, the dominant magnetic noise process is the hyperfine interaction between the electron spins and those of the Si-29 and Ge-73 nuclei [2]. Previously, echo sequences [2,3] have proven effective at decoupling the transverse component of these fluctuating gradients. Here, we demonstrate that is possible to construct a complete set of Clifford gates that provides universal control over DFS qubits while simultaneously incorporating gradient compensation echoes. We show blind randomized benchmarking [1] data using this gate-set with baseline single qubit error rates of 1.8e-3 per Clifford gate, evaluated as a function of both the global magnetic field and the idle time between exchange pulses. Despite containing over three times as many pulses, the gradient-compensating Clifford gate-set out-performs our standard Clifford gate-set in a regime of extended idle durations and applied field. These results point toward error compensation of hyperfine effects as a possible avenue for improving operational fidelity in exchange-only quantum computing.

[1] R. Andrews et al., Nature Nano 14, 747-750 (2019)

[2] J. Kerckhoff et al., PRX Quantum 2, 010347 (2021)

[3] B. Sun et al., arxiv: 2208.11784 (2022)