Pulse Shaping for Controlling Gate Sensitivity and Performing Noise Extrapolation

Pulse shaping, which is the modification of the physical waveforms, is often used to control the behavior of quantum technologies. By tailoring the amplitude and phase of pulses, pulse shaping can be utilized to enhance fidelity or adjust the sensitivity of the basic operations in quantum communication and computing. Most modern error mitigation tries its best to avoid pulse shaping, but we are instead introducing it as a tool. Zero noise extrapolation (ZNE), a common error mitigation protocol in quantum computing, was originally implemented using simple pulse shaping based on stretching the gate duration. Extrapolation from long durations to the zero duration limit allowed scientists to estimate circuit outputs as if no time-sensitive decoherence has occured. In this work, we extend ZNE by applying trajectory-based pulse optimization to systematically adjust the sensitivity of gates to common error sources, while preserving gate fidelity. We systematically explored the trade-off between gate duration and error sensitivity. Quantum gate trajectories were simulated and extracted using the Quantum Collocation framework, and used to implement gates with drift errors. With this, we demonstrate that creating shaped pulses that are sensitive or robust to errors successfully improves fidelity of quantum computations.