Behrang Tafreshi | Searcharxiv

arXiv2026

Feynman Tree Theorem and the Gelfand--Yaglom Formula

The Gelfand--Yaglom formula equates the one-loop determinant of a Schr\"odinger operator with Dirichlet boundary conditions to the solution of an initial value problem. Following a suggestion by Polyakov, we provide a new diagrammatic proof of this formula as a direct application of the Feynman Tree Theorem. By cutting the one-loop determinant, we re-express it as a sum of tree diagrams. These trees explicitly encode the solution to the Gelfand--Yaglom initial value problem. We extend this diagrammatic framework to general boundary conditions and comment on a potential generalization to quantum field theory.

hep-th↗

arXiv2025

Pitfalls when tackling the exponential concentration of parameterized quantum models

Identifying scalable circuit architectures remains a central challenge in variational quantum computing and quantum machine learning. Many approaches have been proposed to mitigate or avoid the barren plateau phenomenon or, more broadly, exponential concentration. However, due to the intricate interplay between quantum measurements and classical post-processing, we argue these techniques often fail to circumvent concentration effects in practice. Here, by analyzing concentration at the level of measurement outcome probabilities and leveraging tools from hypothesis testing, we develop a practical framework for diagnosing whether a parameterized quantum model is inhibited by exponential concentration. Applying this framework, we argue that several widely used methods (including quantum natural gradient, sample-based optimization, and certain neural-network-inspired initializations) do not overcome exponential concentration with finite measurement budgets, though they may still aid training in other ways.

quant-ph↗