Tootfinder

A Method for Constructing Quasi-Random Peaked Quantum Circuits
O. G. Udalov
https://arxiv.org/abs/2508.07491 https://arxiv.org/pdf/2508.07491

A Method for Constructing Quasi-Random Peaked Quantum Circuits
An algorithm is proposed for constructing quasi-random "peaked" quantum circuits, i.e., circuits whose final qubit state exhibits a high probability concentration on a specific computational basis state. These circuits consist of random gates arranged in a brick-wall architecture. While the multiqubit state in the middle of the circuit can exhibit significant entanglement, the final state is, with high probability, a predetermined pure bitstring. A technique is introduced to obscure the final b…

Dynamic Features Adaptation in Networking: Toward Flexible training and Explainable inference
Yannis Belkhiter, Seshu Tirupathi, Giulio Zizzo, Merim Dzaferagic, John D. Kelleher
https://arxiv.org/abs/2510.08303

Dynamic Features Adaptation in Networking: Toward Flexible training and Explainable inference
As AI becomes a native component of 6G network control, AI models must adapt to continuously changing conditions, including the introduction of new features and measurements driven by multi-vendor deployments, hardware upgrades, and evolving service requirements. To address this growing need for flexible learning in non-stationary environments, this vision paper highlights Adaptive Random Forests (ARFs) as a reliable solution for dynamic feature adaptation in communication network scenarios. We…

Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix
Tomohiro Hayase, Beno\^it Collins, Ryo Karakida
https://arxiv.org/abs/2510.06685 https:…

Gaussian Equivalence for Self-Attention: Asymptotic Spectral Analysis of Attention Matrix
Self-attention layers have become fundamental building blocks of modern deep neural networks, yet their theoretical understanding remains limited, particularly from the perspective of random matrix theory. In this work, we provide a rigorous analysis of the singular value spectrum of the attention matrix and establish the first Gaussian equivalence result for attention. In a natural regime where the inverse temperature remains of constant order, we show that the singular value distribution of t…

Disorder-mediated synchronization resonance in coupled semiconductor lasers
Li-Li Ye, Nathan Vigne, Fan-Yi Lin, Hui Cao, Ying-Cheng Lai
https://arxiv.org/abs/2509.07302 https://…

Disorder-mediated synchronization resonance in coupled semiconductor lasers
The interplay between disorder and synchronization in nonlinear oscillator networks has long been known to give rise to counterintuitive phenomena, such as disorder-enhanced coherence. We uncover a frequency-disorder mediated synchronization resonance in coupled external-cavity semiconductor diode lasers. Specifically, we find that intrinsic random frequency detuning among the lasers can enhance synchronization, reaching a maximum at an optimal coupling strength in the weak-coupling regime. The…

Convergent points for random power series on the unit circle
Marcus Michelen, Mehtaab Sawhney
https://arxiv.org/abs/2509.02729 https://arxiv.org/pdf/2509.0…

Convergent points for random power series on the unit circle
Consider a random power series of the form $P(z) = \sum_{n\ge 1} \varepsilon_n a_n z^{n}$ where $a_n \in \mathbb{C}$ are deterministic and $\varepsilon_n$ are chosen independently and uniformly at random from $\{\pm 1\}$. Kolmogorov's three-series theorem states that if $\sum_{n} |a_n|^2 = \infty$ then $P(z)$ almost-surely diverges at almost every $z$ with $|z| = 1$. Dvoretzky and Erdős proved in 1959 that if $|a_n| = Ω(1/\sqrt{n})$ then in fact $P$ almost surely…

Cap amplitudes in random matrix models
Kazumi Okuyama
https://arxiv.org/abs/2509.03930 https://arxiv.org/pdf/2509.03930

Cap amplitudes in random matrix models
For general one-matrix models in the large $N$ limit, we introduce the cap amplitude $ψ(b)$ as the expansion coefficient of the 1-form $ydx$ on the spectral curve. We find that the dilaton equation for the discrete volume $N_{g,n}$ of the moduli space of genus-$g$ Riemann surfaces with $n$ boundaries is interpreted as gluing the cap amplitude along one of the boundaries. In this process, one of the boundaries is capped and the number of boundaries decreases by one. In a similar manner, the gen…

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Shedding light on classical shadows: learning photonic quantum states
Hugo Thomas, Ulysse Chabaud, Pierre-Emmanuel Emeriau
https://arxiv.org/abs/2510.07240 https://

Shedding light on classical shadows: learning photonic quantum states
Efficient learning of quantum state properties is both a fundamental and practical problem in quantum information theory. Classical shadows have emerged as an efficient method for estimating properties of unknown quantum states, with rigorous statistical guarantees, by performing randomized measurement on a few number of copies. With the advent of photonic technologies, formulating efficient learning algorithms for such platforms comes out as a natural problem. Here, we introduce a classical sh…

Excitable quantum systems: the bosonic avalanche laser
Louis Garbe, Peter Rabl
https://arxiv.org/abs/2509.05290 https://arxiv.org/pdf/2509.05290

Excitable quantum systems: the bosonic avalanche laser
We investigate the dynamics of a lasing system that is driven by a current of bosonic (quasi-) particles via a dissipative three-mode mixing process. A semi-classical analysis of this system predicts distinct dynamical regimes, where both the cavity mode and the gain medium can undergo lasing transitions. Of particular interest is an intermediate self-pulsing phase that exhibits the characteristics of an excitable system and converts random input signals into separated, quasi-periodic pulses at…