Link prediction with swarms of chiral quantum walks

TL;DR

Chirality is introduced through the addition of random phases in the Hamiltonian generators to enhance the predictive power of quantum walks on complex networks and highlight the versatility of chiral quantum walks and their potential to outperform both classical and non-chiral quantum methods in realistic scenarios, including comparisons between successive versions of evolving databases.

Abstract

Reconstructing protein-protein interaction networks is a central challenge in network medicine, often addressed using link prediction algorithms. Recent studies suggest that quantum walk-based approaches hold promise for this task. In this paper, we build on these algorithms by introducing chirality through the addition of random phases in the Hamiltonian generators. The resulting additional degrees of freedom enable a more diverse exploration of the network, which we exploit by employing a swarm of chiral quantum walks. Thus, we enhance the predictive power of quantum walks on complex networks. Indeed, compared to a non-chiral algorithm, the chiral version exhibits greater robustness, making its performance less dependent on the optimal evolution time--a critical hyperparameter of the non-chiral model. This improvement arises from complementary dynamics introduced by chirality within the swarm. By analyzing multiple phase-sampling strategies, we identify configurations that achieve a practical trade-off: retaining the high predictive accuracy of the non-chiral algorithm at its optimal time while gaining the robustness typical of chirality. Our findings highlight the versatility of chiral quantum walks and their potential to outperform both classical and non-chiral quantum methods in realistic scenarios, including comparisons between successive versions of evolving databases.

Figures (7)

• Figure 1: Radar chart of normalized metrics for each network from Table \ref{['tab:param']}. Each quantity $q\in\{|V|,|E|,\langle k\rangle,\rho,C,A\}$ is normalized through the equation $q^{\rm Norm}=q/q^{\rm max}$, where the maximum is evaluated among all considered networks.
• Figure 2: Performance of link prediction at $10\%$ link removal on the Musculus-HINT network as a function of the number of considered chiral QW's, at fixed $t=1$. Panel (a) shows the number of links correctly predicted (true positives) among the first predicted non-edges with highest score (positives) for a single fold, considering an increasing number of c-QW's with random phases and without the nc-QW's contribution. Panel (b) shows the convergence of the average AuPR from 10-fold cross-validation. The label 'nc' stands for non-chiral; 'c' and 'tot' refer to the chiral case with random phases, respectively with and without the contribution from the nc-QW; the suffix '$\pi/2$' is used to differentiate the case with phases sampled as random multiples of $\pi/2$ rather than from the continuous interval $[-\pi,\pi]$ (with no suffix).
• Figure 3: Evolution in time of the average AuPR on Musculus-HINT obtained through $k$-fold cross-validation for $10\%$, $20\%$ and $50\%$ link removal, as explained in the text. Labels follow the same nomenclature as Fig. \ref{['fig:conv']}; in addition, the suffix '$\pi/8$' indicates the case with phases sampled from the continuous interval $[-\pi/8,\pi/8]$.
• Figure 4: Average AuPR as a function of the fraction of removed links, obtained through repeated $k$-fold cross-validation, as explained in the text. All continuous lines refer to our link prediction algorithm using chiral and non-chiral QW's, while all dashed lines correspond to various other methods from literature. Labels follow the same nomenclature as previous Figures.
• Figure 5: Average AuROC as a function of the fraction of removed links, obtained through repeated $k$-fold cross-validation, as explained in the text. All continuous lines refer to our link prediction algorithm using chiral and non-chiral QW's, while all dashed lines correspond to various other methods from literature. Labels follow the same nomenclature as previous Figures.