Input-dependence in quantum reservoir computing

TL;DR

This paper investigates conditions for input distinguishability in quantum reservoir computing, enhancing the understanding of how quantum systems can reliably process temporal data by ensuring injectivity in their input-output mappings.

Contribution

It introduces conditions that guarantee input sequence distinguishability in quantum reservoirs, focusing on injectivity of reservoir filters, and analyzes a common quantum reservoir model.

Findings

Identified conditions for injectivity in quantum reservoir filters.

Analyzed a widely used quantum reservoir model with input-encoding channels.

Enhanced understanding of input dependence in quantum reservoir computing.

Abstract

Quantum reservoir computing is an emergent field in which quantum dynamical systems are exploited for temporal information processing. In previous work, it was found a feature that makes a quantum reservoir valuable: contractive dynamics of the quantum reservoir channel toward input-dependent fixed points. These results are enhanced in this paper by finding conditions that guarantee a crucial aspect of the reservoir's design: distinguishing between different input sequences to ensure a faithful representation of temporal input data. This is implemented by finding a condition that guarantees injectivity in reservoir computing filters, with a special emphasis on the quantum case. We provide several examples and focus on a family of quantum reservoirs that is much used in the literature; it consists of an input-encoding quantum channel followed by a strictly contractive channel that enforces the echo state and the fading memory properties. This work contributes to analyzing valuable quantum reservoirs in terms of their input dependence.