Quantum Reservoir Autoencoder: Conditions, Protocol, and Noise Resilience

• URL: http://arxiv.org/abs/2602.19700v2
• Date: Fri, 27 Feb 2026 08:37:51 GMT
• Title: Quantum Reservoir Autoencoder: Conditions, Protocol, and Noise Resilience
• Abstract summary: We introduce the emphquantum reservoir autoencoder (QRA), a four-equation encode-decode protocol with cross-key pairing.<n>Using a full XYZ Hamiltonian reservoir with 10 data qubits, the QRA expands the feature dimension to 76 without increasing qubit count.<n>A comprehensive noise analysis across seven conditions and four baseline methods reveals a clear hierarchy: shot noise dominates, depolarizing noise adds a moderate factor, and asymmetric resource allocation yields approximately two orders of magnitude MSE improvement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum reservoir computing (QRC) 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 owing to the recursive nonlinearity of sequential quantum state evolution. We introduce the \emph{quantum reservoir autoencoder} (QRA), a four-equation encode-decode protocol with cross-key pairing, and constructively show that quantum reservoir and key combinations satisfying all four equations exist. Using a full XYZ Hamiltonian reservoir with 10 data qubits, the QRA expands the feature dimension to 76 without increasing qubit count and achieves machine-precision reconstruction (mean-squared error $\mathrm{MSE} \sim 10^{-17}$) for data lengths up to 30 under ideal conditions; the rank condition $\mathrm{dim}(V) \geq N_c$ is identified as a necessary criterion. A comprehensive noise analysis across seven conditions and four baseline methods reveals a clear hierarchy: shot noise dominates, depolarizing noise adds a moderate factor, and asymmetric resource allocation -- 10 shots for encoding, $10^5$ for decoding -- yields approximately two orders of magnitude MSE improvement by exploiting the asymmetric noise roles of the encryption and decryption feature matrices. Under realistic noise the MSE degrades to $10^{-3}$-$10^{-1}$, indicating that error mitigation is needed before practical deployment, but our results establish the feasibility of the QRA as a bidirectional information transformation framework within QRC.

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