Tootfinder

Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
Xiang-Min Yu, Xiang Deng, Wen Zheng, Wei Xin, Tao Zhang, Hanxin Che, Kun Zhou, Haoyu Zhou, Yangyang Ge, Zhenchuan Zhang, Wanli Huang, Haoyang Cai, Xianke Li, Jie Zhao, Xinsheng Tan, Yu Zhang, Shao-Xiong Li, Yang Yu
https://arxiv.org/abs/2507.06860

Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
Qutrit offers the potential for enhanced quantum computation by exploiting an enlarged Hilbert space. However, the synthesis of high-fidelity and fast qutrit gates, particularly for single qutrit, remains an ongoing challenge, as it involves overcoming intrinsic constraints in quantum platforms. Here, we develop a novel framework for the efficient implementation of a single-qutrit gate set via coherent control, leveraging SU(3) dynamics while obviating platform-specific constraints such as aris…

Quadratic units and cubic fields
Florian Breuer, James Punch
https://arxiv.org/abs/2507.06579 https://arxiv.org/pdf/2507.06579…

Quadratic units and cubic fields
We investigate Eisenstein discriminants, which are squarefree integers $d \equiv 5 \pmod{8}$ such that the fundamental unit $\varepsilon_d$ of the real quadratic field $K=\mathbb{Q}(\sqrt{d})$ satisfies $\varepsilon_d \equiv 1 \pmod{2\mathcal{O}_K}$. These discriminants are related to a classical question of Eisenstein and have connections to the class groups of orders in quadratic fields as well as to real cubic fields. We present numerical computations of Eisenstein discriminants up to $10^{1…

Stochastic Quadratic Dynamic Programming
Vincent Guigues, Adriana Washington
https://arxiv.org/abs/2506.07314 https://arxiv.org/pdf/2…

Stochastic Quadratic Dynamic Programming
We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual Dynamic Programming (SDDP) method replacing affine cuts by quadratic cuts. We provide conditions ensuring strong convexity of the recourse functions and prove the convergence of SQDP. In the special case of a single stage deterministic problem, we call QCSC (Quadra…

Sparse Signal Recovery From Quadratic Systems with Full-Rank Matrices
Jinming Wen, Yi Hu, Meng Huang
https://arxiv.org/abs/2507.07557 https://

Sparse Signal Recovery From Quadratic Systems with Full-Rank Matrices
In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m \ll n$). This paper addresses this problem by exploiting signal sparsity. Using tools from algebraic geometry, we derive theoretical recovery guarantees for sparse quadratic systems, showing that $m\ge 2s$ (real case) and $m\ge 4s-2$ (complex case) generic me…

Maximal curves with respect to quadratic extensions over finite fields
Yves Aubry (IMATH, I2M, UTLN), Fabien Herbaut (UCA INSPE, UniCA, IMATH), Julien Monaldi (IMATH)
https://arxiv.org/abs/2506.08603

Maximal curves with respect to quadratic extensions over finite fields
We propose a detailed study of a canonical bound which relates the numbers of rational points of a curve over a finite field with that over its quadratic extension. Alternative proofs which relate to the variance enable to complete the inequality in a symmetrical way and to obtain optimal refinements. We focus on the curves reaching the bound, which we call Diophantinemaximal curves. We provide different characterizations and stress natural links with the curves which attain the Ihara bound. As…

Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature
Kazuyuki Yagasaki
https://arxiv.org/abs/2506.08046 https:/…

Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature
We study the solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature when the inverse scattering transform (IST) is applied. It is a key to solve the Schrödinger equation appearing in the Lax pair in application of the IST. We show that the Schrödinger equation is always integrable in the sense of differential Galois theory, i.e., solvable by quadrature, if and only if the meromporphic potential is reflectionless, under the condition that the potential…

Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations
Thomas Gamet (UMPA-ENSL)
https://arxiv.org/abs/2506.08590 https://

Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations
In this article, we study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free energy and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian via Bogoliubov transformations, and the diagonalized Hamiltonian is easier to study. We show a renormalization of both the energy and the coupling constant depending on the form factor of the interaction.

Stark-Coleman Invariants and Quantum Lower Bounds: An Integrated Framework for Real Quadratic Fields
Ruopengyu Xu, Chenglian Liu
https://arxiv.org/abs/2506.07640

Stark-Coleman Invariants and Quantum Lower Bounds: An Integrated Framework for Real Quadratic Fields
Class groups of real quadratic fields represent fundamental structures in algebraic number theory with significant computational implications. While Stark's conjecture establishes theoretical connections between special units and class group structures, explicit constructions have remained elusive, and precise quantum complexity bounds for class group computations are lacking. Here we establish an integrated framework defining Stark-Coleman invariants $κ_p(K) = \log_p \left( \frac{\varepsilon_…

Quadratic Extended and Unscented Kalman Filter Updates
Simone Servadio, Chiran Cherian
https://arxiv.org/abs/2506.06256 https://arxiv…

Quadratic Extended and Unscented Kalman Filter Updates
Common filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively, but remain linear estimators, meaning that the state estimate is a linear function of the measurement. This paper proposes a quadratic approximation of the optimal estimator, creating the Quadratic Extended and Quadratic Unscented Kalman Filter. These retain…

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…