Constructing Noise-Robust Quantum Gates via Pontryagin's Maximum Principle

TL;DR

This paper introduces a geometric optimal control framework using Pontryagin's maximum principle to design smooth, noise-robust quantum gates applicable to complex multi-qubit systems, surpassing traditional dynamical decoupling methods.

Contribution

It develops a general, scalable method for synthesizing noise-resistant quantum control pulses without heuristic assumptions, applicable to arbitrary quantum systems and disturbances.

Findings

Framework successfully designs robust quantum gates

Applicable to multi-qubit and multi-level systems

Eliminates heuristic assumptions in pulse design

Abstract

Reliable quantum information technologies depend on precise actuation and techniques to mitigate the effects of undesired disturbances such as environmental noise and imperfect calibration. In this work, we present a general framework based in geometric optimal control theory to synthesize smooth control pulses for implementing arbitrary noise-robust quantum gates. The methodology applies to generic unitary quantum dynamics with any number of qubits or energy levels, any number of control fields, and any number of disturbances, extending existing dynamical decoupling approaches that are only applicable for limited gate sets or small systems affected by one or two disturbances. The noise-suppressing controls are computed via indirect trajectory optimization based on Pontryagin's maximum principle, eliminating the need to make heuristic structural assumptions on parameterized pulse envelopes.