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

Understand

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.