Quantum Reservoir Autoencoder: Conditions, Protocol, and Noise Resilience

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.