Quantum Reservoir Autoencoder: Conditions, Protocol, and Noise Resilience

TL;DR

This paper introduces a quantum reservoir autoencoder that enables bidirectional data transformation, demonstrating high accuracy under ideal conditions and analyzing noise effects, with implications for quantum machine learning.

Contribution

The paper presents the first quantum reservoir autoencoder protocol with empirical validation, addressing noise resilience and revealing the importance of iterative processing over feature dimension.

Findings

Achieves mean-squared error of ~10^{-17} under ideal conditions.

Degradation of MSE to 10^{-3}--10^{-1} under realistic noise.

Iterative protocol structure is the main noise bottleneck.

Abstract

Quantum reservoir computing exploits fixed quantum dynamics and a trainable linear readout to process temporal data, yet reversing the transformation -- reconstructing the input from the reservoir output -- has been considered intractable due to the recursive nonlinearity of sequential quantum state evolution. We introduce the quantum reservoir autoencoder, a four-equation encode--decode protocol with cross-key pairing, and constructively empirically demonstrate that satisfying reservoir--key combinations can be found using a full XYZ Hamiltonian reservoir (10~data qubits, feature dimension~76, 16~random Hamiltonian realizations). Under ideal conditions the mean-squared error (MSE) reaches ${\sim}10^{-17}$ for data lengths up to 30; under shot noise (1\,000~shots) and depolarizing noise ($p = 0.005$), the MSE degrades to $10^{-3}$--$10^{-1}$. Asymmetric resource allocation -- 10~shots for encoding, $10^5$ for decoding -- yields a 102-fold MSE improvement (16~seeds $\times$ 3~trials). Comparison of single-body features (dimension~31) with the full feature set and six baselines identifies the iterative protocol structure -- not the feature dimension -- as the dominant noise bottleneck: baselines solving the linear system in a single step retain machine precision under identical noise, whereas per-iteration noise inconsistency in the coupled solver limits the MSE to ${\sim}10^{-1}$. The current protocol requires plaintext access during decoder training, restricting practical deployment. These results establish a proof-of-concept for bidirectional information transformation within quantum reservoir computing and identify iterative noise mismatch and blind decryption as the principal open challenges.