Quantum Reservoir Computing in ordered atomic lattices

Quantum reservoir computing (QRC) exploits the dynamical properties of quantum systems for machine learning tasks.  Building upon classical reservoir computing, Fujii and Nakajima [PRApp2017] showed the learning capabilities in temporal tasks of a quantum disordered Ising model. Since their seminal work, the field has rapidly evolved for the potential of exploiting the large Hilbert space of quantum states to process classical and quantum inputs data, as well as for fast and easy training. As shown in [Martínez-Peña PRL2021], the working dynamical regime of the reservoir is a fundamental factor in achieving high computational capabilities. Indeed, the ergodic phase is much more expressive than the many-body localization phase. While all the existing literature about QRC is based on disordered systems, which are good candidates to work in the ergodic phase. In this work, we consider a reservoir made of a regular Bose-Hubbard chain in different (Mott-insulator and the superfluid) regimes. We show that disorder is not a necessary condition for QRC, which can facilitate future experiments on real quantum devices. Moreover, we provide strong evidence that optimal performance of the algorithm is achieved in a chaotic dynamical region that emerges for Hamiltonian parameters corresponding to the transition from the superfluid to the Mott insulator phase.