Potential and limitations of quantum extreme learning machines

TL;DR

This paper develops a framework to understand the capabilities and limitations of quantum reservoir computers and quantum extreme learning machines, highlighting their potential for quantum state estimation and system characterization.

Contribution

It introduces a concise modeling approach for QRCs and QELMs using effective measurements and analyzes their information retrieval capabilities.

Findings

QELMs can be modeled via effective measurements.

The training process of QELMs parallels measurement reconstruction.

The framework suggests QELMs are resilient to noise and imperfections.

Abstract

Quantum reservoir computers (QRC) and quantum extreme learning machines (QELM) aim to efficiently post-process the outcome of fixed -- generally uncalibrated -- quantum devices to solve tasks such as the estimation of the properties of quantum states. The characterisation of their potential and limitations, which is currently lacking, will enable the full deployment of such approaches to problems of system identification, device performance optimization, and state or process reconstruction. We present a framework to model QRCs and QELMs, showing that they can be concisely described via single effective measurements, and provide an explicit characterisation of the information exactly retrievable with such protocols. We furthermore find a close analogy between the training process of QELMs and that of reconstructing the effective measurement characterising the given device. Our analysis paves the way to a more thorough understanding of the capabilities and limitations of both QELMs and QRCs, and has the potential to become a powerful measurement paradigm for quantum state estimation that is more resilient to noise and imperfections.