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We propose a scheme for dispersive readout of stored energy in one mode of anonlinear superconducting microwave ring resonator by detection of thefrequency shift of a second mode coupled to the first via a Kerr nonlinearity.Symmetry is used to enhance the device responsivity while minimizing selfnonlinearity of each mode. Assessment of the signal to noise ratio indicatesthat the scheme will function at the single photon level, allowing quantumnon-demolition measurement of the photon number state of one mode. Experimentaldata from a simplified version of the device demonstrating the principle ofoperation are presented.

Exploiting Kerr Cross Non-linearity in Circuit Quantum Electrodynamics for Non-demolition Measurements