Minimizing spectator errors with optimal control pulse engineering

Spectator errors are a type of coherent, off-resonant error that occur when two qubits with nearby resonant frequencies interact, often due to classical cross-talk or a quantum-mechanical fixed couplings on a device [1]. These errors violate common assumptions about Markovianity usually made in QCVV and QEC protocols and occur at error rates of < 1e-4 on modern devices. While these error rates are relatively low, they will become more essential to address with increasing device complexitity and decreasing overall error rates. To date, there lacks any sort of method to correct off-resonant spectator errors. Here, we use optimal control theory (OCT) to numerically engineer $X_{pi/2}$ pulses that are robust against ZX, XZ, and IX spectator interactions and calibrate the pulse on an IBM test device using the dimensional reduction method developed by our group. We demonstrate a successful implementation of this pulse using the phase-sweep spectroscopy amplification experiment developed in [1] and perform randomized benchmarking to demonstrate that the numerically optimized gate has a comparable or better error rate compared to prototypical DRAG pulses. This result thus showcases the promise for OCT to address non-Markovian spectator errors for which there is no known analytical solution, and highlights the application of OCT designed gates on a real device.

[1] https://arxiv.org/abs/2302.10881