Three-qubit direct dispersive parity measurement with Tunable Coupling Qubits

Understand

We consider the direct three-qubit parity measurement scheme with two measurement resonators, using circuit quantum electrodynamics to analyze its functioning for several different types of superconducting qubits.

• We find that for the most common, transmon-like qubit, the presence of additional qubit-state dependent coupling terms of the two resonators hinders the possibility of performing the direct parity measurement.
• We show how this problem can be solved by employing the Tunable Coupling Qubit (TCQ) in a particular designed configuration.
• In this case, we effectively engineer the original model Hamiltonian by cancelling the harmful terms.