Quantum Reservoir Autoencoder for Blind Decryption: Two-Phase Protocol and Noise Resilience

Abstract

We instantiate the quantum reservoir autoencoder (QRA) with a noise-induced reservoir employing reset noise channels and address two open problems: noise-resilient reversibility and blind decryption. For a single-ciphertext protocol with 10 data qubits and random (non-optimized) reset probabilities, the open-system reservoir suppresses shot-noise sensitivity by ten orders of magnitude, yielding mean-squared error (MSE) $\sim 10^{-14}$ compared with $\sim 10^{-3}$ without reset channels ($N_{\mathrm{shots}} = 1000$). A two-phase protocol trains per-position decoding weights from $M$ shared training plaintexts and decrypts previously unseen messages at MSE $\sim 10^{-4}$, with no statistically significant performance difference among ideal, shot-noise, and reset-plus-shot-noise conditions ($p > 0.05$, 16 seeds). Experiments at $N_q = 5$, 7, and 10 reveal a sharp phase transition at plaintext length $N_c \approx N_q(N_q{+}1)/2 + 8$, providing a design rule for the minimum qubit count. Two blind decoder variants that lack ground-truth targets -- a single-ciphertext cross-path iteration (MSE $\approx 0.3$) and a multi-sample regression variant (MSE $\approx 0.53$, worse than random) -- establish that shared training data is the irreducible requirement for blind decryption. A comparison with variational quantum circuit baselines shows that the fixed-reservoir analytic-readout architecture is dramatically more noise-robust: a quantum recurrent neural network protocol is completely destroyed under depolarizing noise, whereas the QRA remains invariant.