Quantum state classification using the inherent nonlinearity of a SNAIL quantum-limited amplifier

We discuss the implementation of a quantum non-linear processing scheme (arXiv:2409.03748) through a two-SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements) oscillator system. In this scheme, SNAIL1 acts as a state generator that generates on demand one of two squeezed vacuum states with orthogonal squeezing directions, while SNAIL2 is used to classify the state generated. Numerical evidence is presented that a non-zero non-linearity in SNAIL2 is required to carry out the task with high fidelity. In this regime, SNAIL2 acts as a quantum non-linear processor that can infer higher-order features (here, second order) of an incident quantum signal, concentrating them into linearly-measurable observables, a transduction not possible using linear amplifiers. We discuss the optimization of the system parameters within a realistic model of the measurement chain for sample-efficient classification.