Real-time compensation of flux pulse distortions for the control of superconducting qubits

High-fidelity two-qubit gates between superconducting qubits have previously been realized by tuning the qubit frequencies with short flux pulses. However, distortions in the flux control line complicate the gate tune-up. In particular, the low-frequency response with memory effect lasting up to microseconds leads to disturbances in subsequent pulses and reduces the gate fidelity. In this work we utilize pre-compensation filters applied in real-time on Zurich Instruments arbitrary waveform generators to correct the line response for the entire gate sequence. This significantly reduces time and memory requirements for pre-computing the digital pulse shape compensation during experimental runs. We optimize the digital filter coefficients based on Ramsey measurements of the flux-line response at the qubit position. The corrected step response is verified to be accurate up to 0.5% of a flat step response between 5 ns to 1 µs. Finally, we quantify the improvement in circuit fidelity obtained by response function correction for the execution of VQA algorithms.