Gaussian states are enough for universal and powerful quantum reservoir computing

Trabajo presentado en el 2nd International Workshop on Quantum Network Science (NetSci 2020 Satellite Workshop), celebrado el 18 de spetiembre de 2020.Machine learning tasks where one time series needs to be transformed to another include chaotic time series prediction, restoring a signal transformed by transmission via a noisy channel and approximating a nonlinear function of a time series. The central idea of reservoir computing is to drive a dynamical system with the input time series and train a simple readout mechanism that maps the system observables to desired output. If the observables are (non)linear functions of input, we say there is (non)linear memory. For rich enough dynamics acting as a source of memory, nontrivial information processing can be realized even by a linear function of reservoir observables. This leads to simple and fast training, a major advantage over alternative machine learning solutions. In the past few years proposals have been made to harness the dynamics of quantum many-body systems for reservoir computing. We establish the potential of continuous-variable Gaussian states in performing reservoir computing with linear systems. The model consists of a network of interacting quantum harmonic oscillators where the state of a subset of oscillators is periodically reset according to input, while the output is taken to be a trained function of the observables of the rest of the network, playing the role of the reservoir. We show that encoding the classical input into quantum states acts as both a source and means to control nonlinear memory, even when the readout is linear in reservoir observables. Another source of nonlinear memory is provided by correlations in reservoir observables. We verify that this is enough to succeed in many typical reservoir computing tasks while keeping the readout linear. We furthermore show that thanks to certain properties of the reservoir memory, letting the readout be polynomial in reservoir observables makes even universal time series processing, i.e. universal reservoir computing, possible both in classical and quantum regime. In stark contrast with quantum computing with continuous-variable systems where it is well-known that Gaussian resources are not enough for universality, our results show that universal reservoir computing does not require non-Gaussian resources or nonlinearity in the Hamiltonian, increasing its feasibility in state-of-the-art optical platforms