Quantum Reservoir Autoencoder: Conditions, Protocol, and Noise Resilience

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.