Composite quantum gates simultaneously compensated for multiple errors

TL;DR

This paper introduces composite quantum gate sequences that simultaneously correct multiple systematic control errors, enhancing fidelity and robustness in quantum operations.

Contribution

The authors develop new composite pulse sequences using derivative-based cancellation and optimization, achieving higher-order error suppression for single-qubit gates.

Findings

Symmetric five-pulse solutions cancel first-order errors.

Longer sequences up to 15 pulses improve error suppression.

Standard sequences are special cases of the new solutions.

Abstract

Systematic control errors remain a primary obstacle to realizing high-fidelity single-qubit gates. We introduce composite pulse sequences that implement X and Hadamard gates while simultaneously compensating amplitude (Rabi-frequency), detuning (frequency), and duration errors. Our construction uses two complementary strategies: (i) derivative-based cancellation of error terms in the full unitary (not just the transition probability), formulated via the Cayley-Klein parametrization, and (ii) direct minimization of the average gate infidelity over prescribed error ranges. We derive symmetric five-pulse solutions with closed-form phases that cancel all first-order terms (including the mixed derivative), and numerically optimize longer sequences -- up to 15 pulses -- to achieve higher-order suppression. We also show that standard ``universal'' five-pulse sequences (U5a/U5b) emerge as simple phase-shifted instances of our symmetric solutions, yielding broad robustness to both detuning and amplitude errors. Finally, we construct variable-area sequences for $R_x(\pi/2)$, which, up to virtual Z rotations, benchmark the Hadamard gate. Across all families we observe the expected trade-off between sequence length and robustness window, with substantial boosts in fidelity over large error domains.