Phase-Encoded Weak Signal Classification Using Quantum Nonlinear Amplifiers

Abstract

Classification of weak stochastic signals poses a significant challenge in both quantum and classical computing. For tasks such as low energy computing or quantum state classification, conventional CMOS gates and superconducting dispersive readout either require external mean-preserving linear amplification or postprocessing analysis to extract information out of low signal-to-noise ratio signals. In this work we propose a Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL)-based physical nonlinear processor for classification of weak stochastic signals. Rather than delineating classes by first-order moments and performing mean-preserving amplification, we explore two input classes that share identical mean amplitudes and instead are solely distinguished by the orientation of their noise geometry. This form of phase encoding makes their classification impossible under conventional linear measurement schemes. However, by leveraging the tunable third and fourth order nonlinearities of the SNAIL device, we demonstrate that this phase difference can be mapped into linearly separable mean amplitude shifts upon output, enabling built-in on-chip state classification without external nonlinear post-processing. Using theoretical modeling and numerical simulation, we characterize the input-output dynamics of the device under linear parametric amplification, and observe the covariance structure of the output modes. We then introduce the fourth-order Kerr nonlinearity and evaluate binary classification fidelity using Fisher discriminant analysis and a trainable linear post-processor. In the fully linear case, the device acts as a mean-preserving amplifier and classifies at a probabilistic level with fidelity of around 50%, while activating the Kerr nonlinearity yields classification of 97.95% ± 0.926%. This result demonstrates high-fidelity classification through intrinsic device dynamics, suggesting a path towards implementing physical neural networks that perform low-power, phase-sensitive classification directly in hardware.