Motivated by the problem of graph structure compression under realistic source models, we study the symmetry behavior of preferential and uniform attachment graphs. These are two dynamic models of network growth in which new nodes attach to a constant number $m$ of existing ones according to some attachment scheme. We prove symmetry results for $m=1$ and $2$, and we conjecture that for $m\geq 3$, both models yield asymmetry with high probability. We provide new empirical evidence in terms of graph defect. We also prove that vertex defects in the uniform attachment model grow at most logarithmically with graph size, then use this to prove a weak asymmetry result for all values of $m$ in the uniform attachment model. Finally, we introduce a natural variation of the two models that incorporates preference of new nodes for nodes of a similar age, and we show that the change introduces symmetry for all values of $m$.

We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (MiFGD), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, MiFGD converges provably close to the true density matrix at an accelerated linear rate asymptotically in the absence of experimental and statistical noise, under common assumptions. With this manuscript, we present the method, prove its convergence property and provide the Frobenius norm bound guarantees with respect to the true density matrix. From a practical point of view, we benchmark the algorithm performance with respect to other existing methods, in both synthetic and real (noisy) experiments, performed on the IBM’s quantum processing unit. We find that the proposed algorithm performs orders of magnitude faster than the state-of-the-art approaches, with similar or better accuracy. In both synthetic and real experiments, we observed accurate and robust reconstruction, despite the presence of experimental and statistical noise in the tomographic data. Finally, we provide a ready-to-use code for state tomography of multi-qubit systems.

Qitong Wang, Mohammed J Zaki, Georgios Kollias, Vasileios Kalantzis. Findings of the Association for Computational Linguistics: ACL 2025. 2025.

Subhajit Chaudhury, Payel Das, Sarathkrishna Swaminathan, Georgios Kollias, Elliot Nelson, Khushbu Pahwa, Tejaswini Pedapati, Igor Melnyk, Matthew Riemer. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.