The fastest pulses that implement dynamically corrected gates

TL;DR

This paper develops a geometrical framework to find the fastest and smoothest control pulses for high-fidelity quantum gates that correct for noise, optimizing quantum control under realistic experimental constraints.

Contribution

It introduces a method to derive time-optimal and experimentally feasible smooth pulses for dynamically corrected quantum gates using geometrical optimization.

Findings

Time-optimized pulses outperform traditional sequences under realistic constraints.

Smooth pulses closely approximate the speed of ideal, non-smooth pulses.

The approach enhances quantum gate fidelity by integrating waveform constraints into control design.

Abstract

Dynamically correcting for unwanted interactions between a quantum system and its environment is vital to achieving the high-fidelity quantum control necessary for a broad range of quantum information technologies. In recent work, we uncovered the complete solution space of all possible driving fields that suppress transverse quasistatic noise errors while performing single-qubit operations. This solution space lives within a simple geometrical framework that makes it possible to obtain globally optimal pulses subject to a set of experimental constraints by solving certain geometrical optimization problems. In this work, we solve such a geometrical optimization problem to find the fastest possible pulses that implement single-qubit gates while cancelling transverse quasistatic noise to second order. Because the time-optimized pulses are not smooth, we provide a method based on our geometrical approach to obtain experimentally feasible smooth pulses that approximate the time-optimal ones with minimal loss in gate speed. We show that in the presence of realistic constraints on pulse rise times, our smooth pulses significantly outperform sequences based on ideal pulse shapes, highlighting the benefits of building experimental waveform constraints directly into dynamically corrected gate designs.