Phys Rev A 98, 022121 (2018) arXiv link
Gradual partial-collapse theory for ideal nondemolition longitudinal readout of qubits in circuit QED
Wei Feng1,* , Cheng Zhang2 , Zhong Wang2 , Lupei Qin1 and Xin-Qi Li 1,2,*
1.Center for Joint Quantum Studies and Department of Physics, Tianjin University, Tianjin 300072, China
2. Department of Physics, Beijing Normal University, Beijing 100875, China
* Corresponding Authors: Wei Feng (Email: fwphy@tju.edu.cn) Xin-Qi Li (Email: xinqi.li@tju.edu.cn)
Abstract:
The conventional method of qubit measurements in circuit QED is employing the dispersive regime of qubit cavity coupling, which results in an approximated scheme of quantum nondemolition (QND) readout. This scheme becomes problematic in the case of strong coupling and/or strong measurement drive, owing to the so-called Purcell effect. A recent proposal by virtue of longitudinal coupling suggests a new scheme to realize fast, high-fidelity, and ideal QND readout of qubit state. The aim of the present work is twofold: (i) In parallel to what has been done in the past years for the dispersive readout, we carry out the gradual partial-collapse theory for this recent scheme, in terms of both the quantum trajectory equation and quantum Bayesian approaches. The partial-collapse weak measurement theory is useful for such as the measurement-based feedback control and other quantum applications. (ii) In the physical aspect, we construct the joint qubit-plus-cavity entangled state under continuous measurement and present a comprehensive analysis for the quantum efficiency, qubit-state purity, and signal-to-noise ratio in the output currents. The combination of the joint state and the quantum Bayesian rule provides a generalized scheme of cavity reset associated with the longitudinal coupling, which can restore the qubit to a quantum pure state from entanglement with the cavity states, and thus benefits the successive partial-collapse measurements after qubit rotations.
