Tootfinder

What's my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution
Nicol\'as Quesada
https://arxiv.org/abs/2507.06154 h…

What's my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution
Quadratic bosonic Hamiltonians and their associated unitary transformations form a fundamental class of operations in quantum optics, modeling key processes such as squeezing, displacement, and beam-splitting. Their Heisenberg-picture dynamics simplifies to linear (or possibly affine) transformations on quadrature operators, enabling efficient analysis and decomposition into optical gate sets using matrix operations. However, this formalism discards a phase, which, while often neglected, is ess…

Quadrature rules with few nodes supported on algebraic curves
Cordian Riener, Ettore Teixeira Turatti
https://arxiv.org/abs/2509.06643 https://arxiv.org/pd…

Quadrature rules with few nodes supported on algebraic curves
We investigate quadrature rules for measures supported on real algebraic and rational curves, focusing on the {odd-degree} case \(2s-1\). Adopting an optimization viewpoint, we minimize suitable penalty functions over the space of quadrature rules of strength \(2s-1\), so that optimal solutions yield rules with the minimal number of nodes. For plane algebraic curves of degree \(d\), we derive explicit node bounds depending on \(d\) and the number of places at infinity, improving results of Rien…

Turnpike Property of a Linear-Quadratic Optimal Control Problem in Large Horizons with Regime Switching II: Non-Homogeneous Cases
Hongwei Mei, Rui Wang, Jiongmin Yong
https://arxiv.org/abs/2508.04993

Turnpike Property of a Linear-Quadratic Optimal Control Problem in Large Horizons with Regime Switching II: Non-Homogeneous Cases
This paper is concerned with an optimal control problem for a nonhomogeneous linear stochastic differential equation having regime switching with a quadratic functional in the large time horizon. This is a continuation of the paper \cite{Mei-Wang-Yong-2025}, in which the strong turnpike property was established for homogeneous linear systems with purely quadratic cost functionals. We extend the results to the current situation. It turns out that some of the results are new even for the cases wi…

Joyce structures from quadratic differentials on the sphere
Timothy Moy
https://arxiv.org/abs/2509.05275 https://arxiv.org/pdf/2509.05275

Joyce structures from quadratic differentials on the sphere
Motivated by known examples of Joyce structures on spaces of meromorphic quadratic differentials, we consider the isomonodromic deformations of particular second-order linear ODEs with rational potential. We show the infinitesimal isomonodromic deformations are the kernel of a closed $2$-form arising from the intersection pairing of an algebraic curve defined by the potential. This observation enables us to construct Joyce structures on a class of moduli spaces of meromorphic quadratic differen…

A Predictive and Sampled-Data Barrier Method for Safe and Efficient Quadrotor Control
Ming Gao, Zhanglin Shangguan, Shuo Liu, Liang Wu, Bo Yang, Wei Xiao
https://arxiv.org/abs/2510.05456

A Predictive and Sampled-Data Barrier Method for Safe and Efficient Quadrotor Control
This paper proposes a cascaded control framework for quadrotor trajectory tracking with formal safety guarantees. First, we design a controller consisting of an outer-loop position model predictive control (MPC) and an inner-loop nonlinear attitude control, enabling decoupling of position safety and yaw orientation. Second, since quadrotor safety constraints often involve high relative degree, we adopt high order control barrier functions (HOCBFs) to guarantee safety. To employ HOCBFs in the MP…

Infinite horizon quadratic backward stochastic differential equations driven by $G$-Brownian motion
Yiqing Lin, Yifan Sun, Falei Wang
https://arxiv.org/abs/2509.05706 https://…

Infinite horizon quadratic backward stochastic differential equations driven by $G$-Brownian motion
The aim is to prove the well-posedness of infinite horizon backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with quadratic generators. To this end, we provide a full construction of explicit solutions to linear $G$-BSDEs with unbounded coefficients and the linearization method under the quadratic assumption. In addition, the comparison theorems for both finite and infinite horizon $G$-BSDEs are established.

From arcs to curves: quadratic growth of 1-systems
Tarik Aougab, Jonah Gaster
https://arxiv.org/abs/2508.05555 https://arxiv.org/pdf/2508.05555

From arcs to curves: quadratic growth of 1-systems
We show that the largest size of a collection of simple closed curves pairwise intersecting at most once on an orientable surface of Euler characteristic $χ$ grows quadratically in $|χ|$. This resolves a longstanding question of Farb-Leininger, up to multiplicative constants. Inspired by the work of Przytycki in the setting of arcs, we introduce the concepts of \textit{almost nibs}, \textit{flowers}, and \textit{stem systems} in order to account for how certain polygons built from p…

Millions of inequivalent quadratic APN functions in eight variables
Christof Beierle, Philippe Langevin, Gregor Leander, Alexandr Polujan, Shahram Rasoolzadeh
https://arxiv.org/abs/2508.04644

Millions of inequivalent quadratic APN functions in eight variables
The only known example of an almost perfect nonlinear (APN) permutation in even dimension was obtained by applying CCZ-equivalence to a specific quadratic APN function. Motivated by this result, there have been numerous recent attempts to construct new quadratic APN functions. Currently, 32,892 quadratic APN functions in dimension 8 are known and two recent conjectures address their possible total number. The first, proposed by Y. Yu and L. Perrin (Cryptogr. Commun. 14(6): 1359-1369, 2022), sug…

Fast and Robust Non-Adiabatic Holonomic Gates for Qutrit Systems
Jie Lu, Jie-Dong Huang, Yang Qian, Ying Yan
https://arxiv.org/abs/2510.05905 https://arxiv…

Fast and Robust Non-Adiabatic Holonomic Gates for Qutrit Systems
Motivated by shortcuts to adiabaticity, we develop a framework that combines inverse engineering with time-dependent perturbation theory to implement non-adiabatic holonomic quantum computing (NHQC) in qutrit systems under realistic error sources. We derive analytical conditions that suppress second-order Rabi errors through tailored pulse parameters and eliminate detuning errors via a compensation pulse. Our analysis reveals the cancellation from the compensation pulse, which ensures robust ga…

Provably data-driven projection method for quadratic programming
Anh Tuan Nguyen, Viet Anh Nguyen
https://arxiv.org/abs/2509.04524 https://arxiv.org/pdf/25…

Provably data-driven projection method for quadratic programming
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs…