Probing graph topology from local quantum measurements

TL;DR

The intrusion strategy is inspired by extreme learning and quantum reservoir computing and combines short-time quantum evolution with a non-iterative linear readout with trainable weights and suggests new strategies for intrusion detection and structural diagnostics in future quantum Internet infrastructures.

Abstract

We show that global properties of an unknown quantum network, such as the average degree, hub density, and the number of closed paths of fixed length, can be inferred from strictly local quantum measurements. In particular, we demonstrate that a malicious agent with access to only a small subset of nodes can initialize quantum states locally and, through repeated short-time measurements, extract sensitive structural information about the entire network. The intrusion strategy is inspired by extreme learning and quantum reservoir computing and combines short-time quantum evolution with a non-iterative linear readout with trainable weights. These results suggest new strategies for intrusion detection and structural diagnostics in future quantum Internet infrastructures.

Figures (3)

• Figure 1: Schematic of the learning protocol. A quantum excitation is initialized on a subset of accessible nodes (red) within a larger network of unknown structure encoded by the adjacency matrix $A$ and let evolve. Site occupations $p_i(t_k)$ on the monitored nodes are recorded at successive time steps. The resulting input vector $\boldsymbol{x}$ feeds a linear readout trained to infer global observables such as $\mathrm{Tr}(A^k)$, hub density, network size, and information leakage parameter $\Gamma$. The method enables inference of the network topology from local quantum measurements.
• Figure 2: Prediction of the leakage strength parameter $\Gamma$. Each marker denotes one data instance (i.e. one sample) for which $\Gamma_{\rm true}$ (horizontal axis) is compared to $\Gamma_{\rm pred}$ (vertical axis). In panel (a) the points refer to the training set, while in panel (b) to the test set. The solid diagonal line indicates the ideal relation $\Gamma_{\rm pred} = \Gamma_{\rm true}$. The mean absolute percentage error (MAPE) is $13.53\%$ on the training set and $2.14\%$ on the test set. The relative high MAPE in training is mainly due to larger relative errors for very small and very large values of $\Gamma$, which are absent in the test set, thus resulting in a more accurate performance.
• Figure 3: Robustness analysis of the protocol. (a) Mean absolute percentage error (MAPE) for the prediction of $\mathrm{Tr}[A^2]$ (third row of Table \ref{['tab:results']}) as a function of the number of graph nodes $N$, while keeping fixed the number of monitored sites ($5$). As expected, the performance slightly deteriorates with increasing $N$, yet remains accurate up to $N \approx 230$. (b) MAPE for the prediction of $\mathrm{Tr}[A^2]$ (second row of Table \ref{['tab:results']}) when the theoretical occupation probabilities are perturbed with Gaussian fluctuations of zero mean and the standard deviation $\sqrt{p(1-p)/N_{\text{shot}}}$, with $p$ the theoretical probability and $N_{\text{shot}}$ the number of repeated measurements. Data points and error bars show the mean and standard deviation of the mean over six independent realizations. The performance is already close to the ideal limit for relatively small $N_{\text{shot}}$, and converges to it for $N_{\text{shot}} \sim 3000$.