Universally Robust Quantum Control

TL;DR

This paper develops a method for designing quantum control pulses that are robust against systematic errors, using fidelity susceptibility and unitary 1-designs to enhance error resistance in quantum gates.

Contribution

It introduces a novel control protocol based on superoperator formalism and Haar 1-designs to achieve robustness against systematic errors in quantum systems.

Findings

Control pulses are robust to systematic errors.

The protocol applies to single- and two-qubit gates.

Optimal control sequences mimic Haar 1-designs.

Abstract

We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be expressed in superoperator form and use this to derive control pulses which are robust to any class of systematic unknown errors. The proposed optimal control protocol is equivalent to searching for a sequence of unitaries that mimics the first-order moments of the Haar distribution, i.e. it constitutes a 1-design. We highlight the power of our results for error resistant single- and two-qubit gates.