Predicting Chaotic Systems with Quantum Echo-state Networks

TL;DR

This paper introduces a quantum echo-state network (QESN) that leverages quantum computing to improve time-series prediction of chaotic systems, aiming to reduce reservoir size and enhance efficiency over classical methods.

Contribution

The work presents a novel quantum circuit implementation of echo-state networks that can operate continuously on NISQ devices, potentially outperforming classical reservoirs in complexity and resource requirements.

Findings

QESN can simulate chaotic Lorenz system trajectories.

The quantum model performs well with noisy and noiseless data.

Potential for implementation on NISQ quantum computers.

Abstract

Recent advancements in artificial neural networks have enabled impressive tasks on classical computers, but they demand significant computational resources. While quantum computing offers potential beyond classical systems, the advantages of quantum neural networks (QNNs) remain largely unexplored. In this work, we present and examine a quantum circuit (QC) that implements and aims to improve upon the classical echo-state network (ESN), a type of reservoir-based recurrent neural networks (RNNs), using quantum computers. Typically, ESNs consist of an extremely large reservoir that learns high-dimensional embeddings, enabling prediction of complex system trajectories. Quantum echo-state networks (QESNs) aim to reduce this need for prohibitively large reservoirs by leveraging the unique capabilities of quantum computers, potentially allowing for more efficient and higher performing time-series prediction algorithms. The proposed QESN can be implemented on any digital quantum computer implementing a universal gate set, and does not require any sort of stopping or re-initialization of the circuit, allowing continuous evolution of the quantum state over long time horizons. We conducted simulated QC experiments on the chaotic Lorenz system, both with noisy and noiseless models, to demonstrate the circuit's performance and its potential for execution on noisy intermediate-scale quantum (NISQ) computers.