# Linear feedback stabilization of a dispersively monitored qubit

## TL;DR

This paper demonstrates a feedback control method that stabilizes a dispersively monitored qubit near a target state by linearly feeding measurement records into the drive, accounting for real-world experimental imperfections.

## Contribution

It introduces a novel linear feedback scheme for dispersively monitored qubits that enhances state stabilization, including analysis of practical nonidealities.

## Key findings

- Feedback effectively stabilizes the qubit state near the target.
- Feedback delay significantly impacts stabilization performance.
- Optimal stabilization occurs when collapse timescale exceeds feedback delay.

## Abstract

The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative, and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse timescale to be long compared to the feedback delay yields the best stabilization.