# Nonlinear Parity Readout with a Microwave Photodetector. (arXiv:1801.00713v1 [quant-ph])

Robust high-fidelity parity measurment is an important operation in many
applications of quantum computing. In this work we show how in a circuit-QED
architecture, one can measure parity in a single shot at very high contrast by
taking advantage of the nonlinear behavior of a strongly driven microwave
cavity coupled to one or multiple qubits. We work in a nonlinear dispersive
regime treated in an exact dispersive transformation. We show that appropriate
tuning of experimental parameters leads to very high contrast in the cavity and
therefore to a high efficiency parity readout with a microwave photon counter
or another amplitude detector. These tuning conditions are based on
nonlinearity and are hence more robust than previously described linear tuning
schemes. In the first part of the paper we show in detail how to achieve this
for two qubit parity measurements and extend this to $N$ qubits in the second
part of the paper. We also study the QNDness of the protocol.