Control limit for the quantum state preparation under stochastic control errors

TL;DR

This paper derives a computable lower bound on the fidelity between ideal and error-affected quantum states, helping evaluate the impact of stochastic control errors in quantum state preparation.

Contribution

It introduces a new lower bound for fidelity under stochastic control errors, enabling analysis without full stochastic dynamics, advancing quantum control robustness assessment.

Findings

The bound accurately predicts the effect of control errors on fidelity.

The method is computationally efficient and applicable to various quantum control scenarios.

Quantitative evaluation of success probability under control errors is demonstrated.

Abstract

We investigate the effect of stochastic control errors on the Hamiltonian that controls a closed quantum system. Quantum information technologies require careful control for preparing a desired state used as an information resource. However, because the stochastic control errors inevitably appear in realistic situation, it is difficult to completely implement the control Hamiltonian. Under this error, the actual performance of quantum control is far away from the ideal one, and thus it is of great importance to evaluate the effect of the control errors. In this paper, we derive a lower bound of the fidelity between two closed quantum systems obeying the dynamics with and without errors. This bound reveals a reachable and unreachable set of the controlled quantum system under stochastic noises. Also, it is easily computable without considering the stochastic process and needing the full dynamics of the states. We demonstrate the actual performance of this bound via a simple control example. Furthermore, based on this result, we quantitatively evaluate the probability of obtaining the target state in the presence of control errors.