Optimized reconstruction methods for imaging squeezed microwave states*

Superconducting parametric amplifiers (paramps) are essential tools for quantum-limited measurement of superconducting qubits. A central feature of these devices is that they can ideally amplify information in one quadrature without adding noise while simultaneously squeezing fluctuations in the orthogonal quadrature. At microwave frequencies, moment-based reconstruction techniques are commonly utilized to image such squeezed states. Motivated by a desire to characterize and improve paramp squeezing performance, we have developed simulations to understand the application of these reconstruction techniques, with a focus on determining their performance at large signal gains where the amplifier output field becomes non-Gaussian. We make comparisons of this analysis to experimental data. We have also developed a complementary imaging method based on deconvolution techniques that is effective for high signal-to-noise ratios. This method benefits from a simple implementation and provides a best estimate for the output field Q function. We discuss experimental implementations of these techniques facilitated by the use of a broadband parametric amplifier.