Parity measurements using parametrically driven resonators: Part I*

Multi-qubit parity measurements are indispensable for quantum error correction. A possible way to realize these is by homodyne measurement of the field of a cavity which is dispersively coupled to multiple qubits. However such an interaction can lead to dephasing within the parity subspace and results in only half-parity measurement. With the aim of overcoming this shortcoming, in this talk we will introduce the parametrically driven nonlinear resonator as an alternate approach to measure multi-qubit parity. With analytical results, we will show that this approach leads to significant reduction of parity-subspace dephasing making full-parity measurements possible.