Quantum Non-demolition Measurement of the Transverse Component of a Qubit Using a Dissipative SNAIL Coupler*

Quantum Non-Demolition (QND) measurements of qubit arrays along combinations of both the transverse (x, y) and longitudinal (z) axes are commonly needed in quantum error correction. In this work we have designed and implemented a QND transverse axes measurement protocol on a transmon qubit by parametrically pumping a lossy, three-wave SNAIL coupler at the sum and difference frequencies between the qubit and the SNAIL mode. Such a two-tone pump effectively projects the qubit onto a transverse axis determined by the pump phases, and creates coherent light in the SNAIL mode with a phase that is conditional on whether the qubit is, for instance, in the +x or -x eigenstate. This resultant x-basis measurement result is collected by demodulating the SNAIL output signal.  Unlike usual dispersive measurement based on the Jaynes–Cummings Hamiltonian, this interaction is off when the drives are removed, which can enhance qubit coherence by rendering the transmon insensitive to thermal photons in the readout mode.  We will present the measurement frame tune-up protocol, experiment data on measurement fidelity and efficiency, as well as the prospects for measuring multi-qubit operators by parametrically linking more than one qubit to a single SNAIL.