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.

Figures (19)

• Figure 1: Single-C protocol under ideal conditions (Exp 1, Path 1). Decryption MSE versus ALS iteration for $N_c = 5$ to 35. Shaded regions indicate $\pm 1$ standard deviation across 16 seeds $\times$ 3 trials. All curves converge to machine precision within one iteration.
• Figure 2: Single-C protocol under shot noise (Exp 3, $N_{\mathrm{shots}} = 1000$, Path 1). The MSE reaches a noise floor after $\sim$5 iterations. Shaded regions indicate $\pm 1$ standard deviation.
• Figure 3: Single-C protocol under reset + shot noise (Exp 5, Path 1). Despite the presence of both reset noise channels and shot noise, the MSE reaches $\sim 10^{-14}$--$10^{-12}$, close to the ideal limit. Shaded regions indicate $\pm 1$ standard deviation across 16 seeds $\times$ 3 trials.
• Figure 4: Unified comparison of Single-C final MSE (mean $\pm$ s.d.) under three noise conditions. The three regimes span 15 orders of magnitude, with Reset+Shot (QRA) achieving precision within 3 orders of the Ideal.
• Figure 5: Two-phase protocol under ideal conditions (Exp 2, Path 1). Blind decryption MSE versus number of training plaintexts $M$, for $N_c = 5$ to 35. Shaded regions indicate $\pm 1$ standard deviation across 16 seeds.