Nonlinear Convergent Dynamics for Temporal Information Processing on Novel Quantum and Classical Devices

Abstract

Reservoir computing is an emerging neuromorphic computing paradigm for temporal processing tasks that is also energy and memory-efficient. It has demonstrated promising performance on chaotic modeling, speech processing and time series prediction. This thesis presents theoretical and experimental studies aimed at ex- panding the toolkit for temporal information processing by utilizing uniformly convergent dynamical systems as reservoir computers. Reservoir computing offloads computations to naturally occurring or engineered nonlinear dynamical systems and typically only a simple readout mechanism is optimized to perform temporal tasks. The uniform convergence property ensures that the computation performed is asymptotically independent of the reservoir computer’s initial condition.

Physical reservoir computers are hardware implementations of reservoir computers for fast signal processing. We propose two families of universal quantum reservoir computers as physical reservoir computers–the Ising quantum reservoir computers and the gate-model quantum reservoir computers–that are both based on uni- formly convergent dissipative quantum dynamics. We demonstrate numerically with the Ising scheme and experimentally with the gate-model scheme, that small and noisy quantum reservoirs can tackle nonlinear temporal tasks.

The study of quantum reservoir computers is followed by a theoretical effort in broadening the applications of reservoir computers. We study a general architecture of reservoir computing, in which reservoir computers governed by different dynamics are interconnected in an output-feedback configuration. This architecture is motivated by the use of nonlinear closed-loop structures to better capture data that demonstrate nonlinear feedback phenomena, akin to the Wiener-Hammerstein feedback model for system identification. A theorem for interconnected reservoir computers to be uniformly convergent is derived. We then show that uniformly convergent reservoir computers with output feedback implement a large family of nonlinear autoregressive models. Finally, we consider the reservoir design problem and propose an efficient algorithm to optimize the reservoir internal parameters, and show the almost sure convergence to a Kuhn-Tucker point under noisy state measurements.