Qubit fidelity distribution under stochastic Schrödinger equations driven by classical noise

Environmental noise affecting controlled quantum systems is typically described by a dissipative Lindblad equation, which captures the system's average state through the density matrix 𝜌. One approach to deriving this equation involves a stochastic operator evolving under white noise in the Schrödinger equation; however, white noise fails to accurately depict real-world noise profiles, where lower frequencies often dominate. This study proposes a method to determine the analytic distribution of qubit fidelities in significant stochastic Schrödinger equation scenarios, with qubits evolving under more realistic noise profiles such as Ornstein-Uhlenbeck noise. This method enables the prediction of the mean, variance, and higher-order moments of qubit fidelities, offering insights crucial for assessing permissible noise levels in prospective quantum computing systems and guiding decisions about control systems procurement. Additionally, these methodologies are essential for optimizing qubit state control affected by classical control system noise.