Sampled-data design for robust control of a single qubit

TL;DR

This paper introduces a sampled-data control method for robustly managing a single qubit's quantum state, accounting for uncertainties and decoherence, with applications in quantum error correction and gate construction.

Contribution

It develops a novel sampled-data control strategy for single qubits that ensures robustness against uncertainties and decoherence, with specific sampling period design and control conditions.

Findings

Designed sampling periods guarantee robustness across different decoherence scenarios.

Presented sufficient conditions for unitary control without decoherence and with amplitude damping.

Applicable to quantum error correction and robust quantum gate construction.

Abstract

This paper presents a sampled-data approach for the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered involving the system Hamiltonian and the coupling strength of the system-environment interaction. Four cases are analyzed in detail including without decoherence, with amplitude damping decoherence, phase damping decoherence and depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required robustness. Two sufficient conditions are presented for guiding the design of unitary control for the cases without decoherence and with amplitude damping decoherence. The proposed approach has potential applications in quantum error-correction and in constructing robust quantum gates.