Time Series Quantum Reservoir Computing with Weak and Projective Measurements

TL;DR

This paper explores measurement protocols in quantum reservoir computing, demonstrating that efficient, online time-series processing is achievable by leveraging weak and projective measurements without sacrificing quantum advantage.

Contribution

It introduces and assesses measurement protocols that preserve reservoir memory and quantum advantage, enabling effective online quantum time-series analysis.

Findings

Two measurement protocols achieve ideal performance in memory and forecasting.

Weak measurements balance information extraction and memory retention.

Fading memory time is crucial for protocol efficiency.

Abstract

Quantum machine learning represents a promising avenue for data processing, also for purposes of sequential temporal data analysis, as recently proposed in quantum reservoir computing (QRC). The possibility to operate on several platforms and noise intermediate-scale quantum devices makes QRC a timely topic. A challenge that has not been addressed yet, however, is how to efficiently include quantum measurement in realistic protocols, while retaining the reservoir memory needed for sequential time series processing and preserving the quantum advantage offered by large Hilbert spaces. In this work, we propose different measurement protocols and assess their efficiency in terms of resources, through theoretical predictions and numerical analysis. We show that it is possible to exploit the quantumness of the reservoir and to obtain ideal performance both for memory and forecasting tasks with two successful measurement protocols. One consists in rewinding part of the dynamics determined by the fading memory of the reservoir and storing the corresponding data of the input sequence, while the other employs weak measurements operating online at the trade-off where information can be extracted accurately and without hindering the needed memory. Our work establishes the conditions for efficient protocols, being the fading memory time a key factor, and demonstrates the possibility of performing genuine online time-series processing with quantum systems.