Preparing squeezed, cat and GKP states with parity measurements

Abstract

Abstract Bosonic modes constitute a central resource in a wide range of quantum technologies, providing long-lived degrees of freedom for the storage, processing, and transduction of quantum information. Such modes naturally arise in platforms including circuit quantum electrodynamics, quantum acoustodynamics, and trapped-ion systems. In these architectures, coherent control and high-fidelity readout of the bosonic degrees of freedom are achieved via coupling to an auxiliary qubit. When operated in the strong dispersive regime, this interaction enables parity measurements of the mode which, in combination with phase-space displacements, constitute a standard experimental tool for full Wigner-function tomography. Here, we propose a protocol based on displaced parity measurements that allows for the preparation of a variety of bosonic quantum states. We demonstrate the generation of squeezed states, achieving ~9 dB of quantum noise reduction after three parity measurements, and larger squeezing with an increasing number of measurements in the lossless case. The technique can be generalized to the preparation of other paradigmatic bosonic states, including cat and Gottesman-Kitaev-Preskill states. Using more general dispersive measurements and displacements, we show that the scheme is universal, such that it is possible to prepare an arbitrary state.