Stochastic Master Equation Analysis of Optimized Three-Qubit Nondemolition Parity Measurement

Abstract

We analyze a direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected/transmitted microwave radiation and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these conditions and we analyze this detrimental effect and show that it can be overcome in the limit of weak measurement signal. Our analysis shows that, with a moderate degree of post-selection, it is possible to achieve post-measurement states with fidelity of order 95%. We believe that this type of measurement could serve as a benchmark for future error-correction protocols in a scalable architecture.

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• Dissipation-induced continuous quantum error correction for superconducting circuits
• Qubit Parity Measurement by Parametric Driving in Circuit QED
• Scalable two- and four-qubit parity measurement with a threshold photon counter
• Three-qubit direct dispersive parity measurement with Tunable Coupling Qubits
• Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis
• Towards a heralded eigenstate preserving measurement of multi-qubit parity in circuit QED
• Gradual partial-collapse theory for ideal nondemolition measurements of qubits in circuit QED