Quantum state-preparation control in noisy environment via most-likely paths

TL;DR

This paper introduces a control strategy for quantum state preparation in noisy environments, leveraging the most-likely noise paths to improve success rates over traditional average-based methods.

Contribution

It proposes a novel control approach based on likelihood of noise, providing analytical solutions and benchmarking against existing methods.

Findings

Most-likely controls yield higher success rates than mean-path controls at strong dephasing.

The method is analytically applied to qubit state preparation under dephasing noise.

Benchmarking shows improved success rates with the proposed approach.

Abstract

Finding controls for open quantum systems needs to take into account effects from unwanted environmental noise. Since actual realizations or states of the noise are typically unknown, the usual treatment for the quantum system's decoherence dynamics is via the so-called Lindblad master equation, which in essence describes an average evolution (mean path) of the system's state affected by the unknown noise. We here consider an alternative view of a noise-affected open quantum system, where the average dynamics can be unravelled into hypothetical noisy quantum trajectories, and propose a control strategy for the state-preparation problem based on the likelihood of noise occurrence. We formulate a stochastic path integral for noise variables whose extremum yields control functions associated with a most-likely noise to achieve target states. As a proof of concept, we apply our method to a qubit-state preparation under dephasing noise and analytically solve for controlled Rabi drives for arbitrary target states. Since the method is constructed based on the probability of noise, we also introduce a fidelity success rate as a measure of the state preparation. We benchmark against the mean-path approaches, e.g., GRAPE and CRAB controls, using both average fidelity and a success-rate metric. While standard mean-path controls maximize average fidelity, most-likely controls achieve higher success rates, especially at strong dephasing.