Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing

Abstract

Quantum reservoir computing aims at harnessing the rich dynamics of quantum systems for machine-learning purposes. It can be used for online time series processing while having a remarkably low training cost. Here, we establish the potential of continuous-variable Gaussian states of linear dynamical systems for quantum reservoir computing. We prove that Gaussian resources are enough for universal reservoir computing. We find that encoding the input into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that the full potential of the proposed model can be reached by encoding to quantum fluctuations, such as squeezed vacuum, instead of classical fields or thermal fluctuations. Our results introduce a research paradigm for reservoir computing harnessing quantum systems and engineered Gaussian quantum states.

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

“…These encodings have been analyzed in the case of single‐mode Gaussian states in harmonic networks in ref. [43], where it was shown that the encoding choice can display a significant effect on the QRC performance (see Section 2.6).…”

“…Starting with classical tasks, there are several recent studies about the performance of quantum reservoirs as substrates for (classical) time‐series processing, [ 33–44,47,52 ] so they are in the CQC class. These include benchmark tasks commonly considered in classical RC such as the timer task (see Section 2.5.2), realizing nonlinear functions of past inputs such as the nonlinear autoregressive moving average (NARMA), [ 69 ] and chaotic time series prediction based on, for example, the Mackey‐Glass system.…”

“…[ 72 ] e) Quantum circuits [ 38,76 ] have been used as a substrate in the IBM platform. [ 39,41 ] f) Continuous‐variable models [ 43,47,76 ] could be engineered in photonic experimental setups as well, [ 77–79 ] that is, by coupling different frequency modes in non‐linear media.…”

“…In particular, the spin‐based implementation is the most analyzed platform for QRC at the moment, [ 34–42 ] with the continuous‐variable systems becoming another promising option. [ 43–45 ] In the context of QELM, both fermionic and bosonic setups have been proposed for instance in entanglement detection [ 46 ] or light field phase estimation. [ 47 ] Inspired by these neuromorphic approaches other quantum tasks have been reported such as quantum states preparation [ 48,49 ] or reconstruction.…”

“…[ 33 ] The extent of this advantage when accessing a large number of output degrees of freedom has been quantified for instance in QRC with spin [ 40 ] as well as Gaussian networks. [ 43 ] While decoherence is a strong limiting factor in gate‐based quantum computing, in principle QRC and QELM are well suited for noisy intermediate‐scale quantum (NISQ). [ 52 ] Furthermore quantum substrates can interact with quantum inputs and are naturally suited for quantum tasks, providing new avenues for edge computing in quantum systems with increasing complexity.…”