Abstract: The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir computing relaxes the need for optimization of intra-network parameters, and is thus particularly attractive for near-term hardware-efficient quantum implementations. However, the complete description of practical quantum reservoir computers requires accounting for their placement in a quantum measurement chain, and its conditional evolution under measurement. Consequently, training and inference has to be performed using finite samples from obtained measurement records. Here we describe a framework for reservoir computing with nonlinear quantum reservoirs under continuous heterodyne measurement. Using an efficient truncated-cumulants representation of the complete measurement chain enables us to sample stochastic measurement trajectories from reservoirs of several coupled nonlinear bosonic modes under strong excitation. This description also offers a rigorous mathematical basis to directly compare the computational performance of a given physical reservoir operated across classical and quantum regimes, considering a variety of practical performance metrics such as fidelity, sample-efficiency, and time-to-solution. Even for a reservoir as small as a single node where entanglement cannot play a role, we show that operation deeper in the quantum regime offers a modest but statistically significant advantage in sample-efficiency for learning Gaussian quantum states that have the same mean but distinct variances. Further, comparing the same metrics we show that certain other state learning tasks are better performed by reservoirs in the classical regime. Our results also identify the vicinity of classical bifurcation points as presenting optimal conditions for nonlinear processing by an oscillator-based quantum reservoir. The considered models are directly realizable in modern circuit QED experiments, while the framework is applicable to more general quantum nonlinear reservoirs.
arXiv:2110.13849
Host: Kanu Sinha/Alicia Kollár