Optimizing a quantum reservoir computer for time series prediction

Abstract

Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient solving of temporal machine learning tasks such as speech recognition, time series prediction and natural language processing. Specifically, we study memory capacity and accuracy of a quantum reservoir computer based on the fully connected transverse field Ising model by investigating different forms of inter-spin interactions and computing timescales. We show that variation in inter-spin interactions leads to a better memory capacity in general, by engineering the type of interactions the capacity can be greatly enhanced and there exists an optimal timescale at which the capacity is maximized. To connect computational capabilities to physical properties of the underlaying system, we also study the out-of-time-ordered correlator and find that its faster decay implies a more accurate memory. Furthermore, as an example application on real world data, we use QRC to predict stock values.

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

“…The value of the classical input, for a normalized continuous variable, or for a binary one, fixes the components, that is, . Subsequent works concerning time‐series predictions have employed a similar input encoding procedure [ 35,40 ] in pure states. An alternative way to encode the classical input is used in refs.…”

“…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.…”

“…Various examples of platforms to be used as quantum substrates for information processing. Two suitable candidates to implement spin‐network models [ 33–37,40,52 ] are a) nuclear magnetic resonance in molecules, [ 51 ] and b) trapped ions. [ 75 ] c) State‐of‐the‐art ultracold atomic setups in optical lattices with bosonic and fermionic species are well‐suited for Bose–Hubbard and Fermi–Hubbard discrete models, [ 46,48–50,62 ] respectively.…”

“…The efforts to analyze and optimize the performance of the original spin model are still ongoing. [ 35,40,42 ] Regarding QELM systems, the universal approximation property of continuous functions has been studied in ref. [80], where several scenarios were considered.…”

“…Since the pioneering proposal of networks of quantum spins as reservoir substrates, [ 33 ] there have been a variety of works exploring the possibilities that quantum mechanics can offer to this research area. 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.…”