Linear feedback stabilization of a dispersively monitored qubit

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.

16 pages, 7 figures

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• Multi-time correlators in continuous measurement of qubit observables
• Past observable dynamics of a continuously monitored qubit
• Continuous measurement of a qudit using dispersively coupled radiation
• Quantum proportional-integral (PI) control
• Stabilizing two-qubit entanglement with dynamically decoupled active feedback
• Quantum dynamics under simultaneous and continuous measurement of noncommutative observables
• Correlators exceeding one in continuous measurements of superconducting qubits
• Bounding fidelity in quantum feedback control: theory and applications to Dicke state preparation