Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis

Abstract

We derive a family of stochastic master equations describing homodyne measurement of multi-qubit diagonal observables in circuit quantum electrodynamics. In the regime where qubit decay can be neglected, our approach replaces the polaron-like transformation of previous work, which required a lengthy calculation for the physically interesting case of three qubits and two resonator modes. The technique introduced here makes this calculation straightforward and manifestly correct. Using this technique, we are able to show that registers larger than one qubit evolve under a non-Markovian master equation. We perform numerical simulations of the three-qubit, two-mode case from previous work, obtaining an average post-measurement state fidelity of $\sim 94\%$, limited by measurement-induced decoherence and dephasing.

22 pages, 9 figures. Comments welcome

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• Recursive approach for non-Markovian time-convolutionless master equations
• Always-On Quantum Error Tracking with Continuous Parity Measurements
• Three-qubit direct dispersive parity measurement with Tunable Coupling Qubits
• Breakdown signatures of the phenomenological Lindblad master equation in the strong optomechanical coupling regime
• Towards a heralded eigenstate preserving measurement of multi-qubit parity in circuit QED