Quantum reservoir computing using weakly-nonlinear Josephson junction networks under homodyne measurement*

We analyze a model for quantum reservoir computing for quantum state classification based on single-shot measurements of a small-scale weakly-nonlinear quantum reservoir computer that is directly coupled to the quantum system of interest. This description is in contrast to more standard approaches where information about the states to be classified is described by ensemble-averaged quantities measured separately and subsequently fed to the reservoir computer. Our coupled model requires a complete quantum-mechanical description of the entire measurement chain undergoing conditional evolution. This description is relevant for experimental realizations of classification tasks based on single-shot readout schemes, and emerges naturally for weakly-nonlinear Josephson-junction networks in the circuit QED architecture under homodyne
measurement. We determine the classification fidelity for coherent as well as squeezed and entangled states as a function of engineerable reservoir hyperparameters, and assess the capabilities of the proposed quantum reservoir computers in the weakly-nonlinear regime.