Designing dynamically corrected gates robust to multiple noise sources using geometric space curves

TL;DR

This paper introduces a geometric framework for designing quantum control fields that simultaneously suppress multiple noise sources, improving the robustness of quantum gates.

Contribution

It develops a general method using space curve formalism to create control schemes that cancel both control field errors and dephasing noise at leading order.

Findings

Derived necessary and sufficient conditions for noise cancellation.

Provided explicit examples of robust control fields.

Linked holonomic evolution to control error suppression.

Abstract

Noise-induced gate errors remain one of the main obstacles to realizing a broad range of quantum information technologies. Dynamical error suppression using carefully designed control schemes is critical for overcoming this challenge. Such schemes must be able to correct against multiple noise sources simultaneously afflicting a qubit in order to reach error correction thresholds. Here, we present a general framework for designing control fields that simultaneous suppress both noise in the fields themselves as well as transverse dephasing noise. Using the recently developed Space Curve Quantum Control formalism, in which robust quantum evolution is mapped to closed geometric curves in a multidimensional Euclidean space, we derive necessary and sufficient conditions that guarantee the cancellation of both types of noise to leading order. We present several techniques for solving these conditions and provide explicit examples of error-resistant control fields. Our work also sheds light on the relation between holonomic evolution and the suppression of control field errors.