Information Theoretical Limits for Quantum Optimal Control Solutions: Error Scaling of Noisy Channels

TL;DR

This paper establishes analytical bounds on the controllability of noisy open quantum systems using information theory, and validates these bounds through numerical simulations and comparison with decoherence models.

Contribution

It introduces information-time bounds for quantum control under noise and demonstrates their accuracy through numerical testing with the dCRAB algorithm.

Findings

Information-time bounds accurately predict control limitations in noisy quantum systems.

The bounds agree well with the Kofman-Kurizki decoherence formula.

Numerical simulations confirm the scaling of control accuracy with noise parameters.

Abstract

Accurate manipulations of an open quantum system require a deep knowledge of its controllability properties and the information content of the implemented control fields. By using tools of information and quantum optimal control theory, we provide analytical bounds (information-time bounds) to characterize our capability to control the system when subject to arbitrary sources of noise. Moreover, since the presence of an external noise field induces open quantum system dynamics, we also show that the results provided by the information-time bounds are in very good agreement with the Kofman-Kurizki universal formula describing decoherence processes. Finally, we numerically test the scaling of the control accuracy as a function of the noise parameters, by means of the dressed chopped random basis (dCRAB) algorithm for quantum optimal control.