Using Noisy Qubits to Achieve Universal Reservoir Computation

Reservoir computing has emerged as an alternative to neural networks that reduces training costs significantly by leveraging a complex dynamical system to enrich the expressive content of the input before the system is trained using simple linear regerssion. An echo state network (ESN) is a type of reservoir computer that also qualifies as a recurrent neural network, in which the reservoir is determined by a set of fixed neural weights and a nonlinear activation function. In previous work, we proved that stochastic ESNs which satisfy certain conditions can form a universal approximating class, meaning that for any given task there will exist some reservoir computer within the class that can perform the task within some arbitrarily chosen error tolerance. In this presentation, I will introduce one such class of stochastic ESNs which we referred to in our previous work as the qubit reservoir network. This ESN is a hybrid design where the application of the weights is performed on classical hardware, while a set of qubits prepared using only 1-qubit rotations provides an activation function. Our design exploits the stochastic nature of the quantum system such that the number of trained weights grows exponentially with the number of qubits. We will discuss the advantages that can be achieved by using currently available NISQ-era qubits in our stochastic ESN versus using classically calculated activation functions in a typical software ESN.