Tootfinder

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Shikher Sharmaa, Pankaj Gautam, Simeon Reich
https://arxiv.org/abs/2506.22391

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution of the equilibrium problem without requiring the Lipschitz continuity of the bifunction or imposing additional conditions on the parameters. We establish convergence results for both algorithms and derive global error bounds along with $R$-linear convergence …

Resource-Efficient Hadamard Test Circuits for Nonlinear Dynamics on a Trapped-Ion Quantum Computer
Eleftherios Mastorakis, Muhammad Umer, Milena Guevara-Bertsch, Juris Ulmanis, Felix Rohde, Dimitris G. Angelakis
https://arxiv.org/abs/2507.19250

Resource-Efficient Hadamard Test Circuits for Nonlinear Dynamics on a Trapped-Ion Quantum Computer
Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations. Here, we propose a low-depth implementation of a class of Hadamard test circuits, complemented by the development of a parameterized quantum ansatz specifically tailored for variational algorithms that exploit the underlying Hadamard test framework. Our find…

A synthetic Lorentzian Cartan-Hadamard theorem
Darius Er\"os, Sebastian Gieger
https://arxiv.org/abs/2506.22197 https://arxiv.or…

A synthetic Lorentzian Cartan-Hadamard theorem
We formulate and prove a synthetic Lorentzian Cartan-Hadamard theorem. This result both transfers the corresponding statement for locally convex metric spaces established by S. Alexander and R. Bishop to the Lorentzian setting, and simultaneously generalizes the smooth Lorentzian theorem discussed by J. Beem and P. Ehrlich to the recently established framework of synthetic Lorentzian geometry. Our approach is based on an appropriate notion of local concavity for Lorentzian (pre-)length spaces, …

Anticoherent $k$-planes and coding techniques for a 3-qubit scheme of universal quantum computing
L. Arag\'on-Mu\~noz, C. Chryssomalakos, A. G. Flores-Delgado, V. Rasc\'on-Barajas, I. V\'azquez Mota
https://arxiv.org/abs/2509.23464

Anticoherent $k$-planes and coding techniques for a 3-qubit scheme of universal quantum computing
Toponomic quantum computing (TQC) employs rotation sequences of anticoherent $k$-planes to construct noise-tolerant quantum gates. In this work, we demonstrate the implementation of generalized Toffoli gates, using $k$-planes of spin systems with $s \geq k + 1$, and of the Hadamard gate for a 3-qubit system, using a spin $s \!= \! 15$ 8-plane. We propose a universal quantum computing scheme for 3-qubit systems (via Hadamard + Toffoli gates) based on coding techniques. A key advantage of this co…

Lensing Without Borders: Measurements of galaxy-galaxy lensing and projected galaxy clustering in DESI DR1
S. Heydenreich, A. Leauthaud, C. Blake, Z. Sun, J. U. Lange, T. Zhang, M. DeMartino, A. J. Ross, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. Cuceu, A. de la Macorra, J. DeRose, Arjun Dey, Biprateep Dey, P. Doel, N. Emas, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, C. Garcia-Quintero, E. Gazta\~naga, S. Gontcho A Gontcho, G. Gutierrez, B. Had…

Lensing Without Borders: Measurements of galaxy-galaxy lensing and projected galaxy clustering in DESI DR1
We present Galaxy-Galaxy Lensing measurements obtained by cross-correlating spectroscopically observed galaxies from the first data release of the Dark Energy Spectroscopic Instrument (DESI) with source galaxies from the Hyper Suprime-Cam Subaru Strategic Survey, the Kilo-Degree Survey, the Sloan Digital Sky Survey, and the Dark Energy Survey. Specifically, we measure the excess surface mass density $ΔΣ$ and tangential shear $γ_\mathrm{t}$ for the Bright Galaxy Sample and Luminous Red Galaxi…

Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators
Habib Ammari, Clemens Thalhammer, Alexander Uhlmann
https://arxiv.org/abs/2509.22417

Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators
We aim to characterise the spectral distributions of bi-infinite, semi-infinite, and finite aperiodic one-dimensional arrays of subwavelength resonators, constructed by sampling from a finite library of building blocks. By adopting the modern formalism of uniform hyperbolicity, we are able to strengthen and rigorously prove a Saxon-Hutner-type result, fully characterising the spectral gaps of the composite bi-infinite aperiodic system in terms of its constituent blocks. Crucial to this approach…

Orthogonal designs and symmetric Hadamard matrices
Dragomir \v{Z}. Djokovi\'c
https://arxiv.org/abs/2508.17141 https://arxiv.org/pdf/2508.17141

Orthogonal designs and symmetric Hadamard matrices
Our main result is the construction of symmetric Hadamard matrices of order q(1 + q) where q is a prime power congruent to 3 mod 8.

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Two bases suffice for QMA1-completeness
Henry Ma, Anand Natarajan
https://arxiv.org/abs/2509.24390 https://arxiv.org/pdf/2509.24390

Two bases suffice for QMA1-completeness
We introduce a basis-restricted variant of the Quantum-k-SAT problem, in which each term in the input Hamiltonian is required to be diagonal in either the standard or Hadamard basis. Our main result is that the Quantum-6-SAT problem with this basis restriction is already QMA1-complete, defined with respect to a natural gateset. Our construction is based on the Feynman-Kitaev circuit-to-Hamiltonian construction, with a modified clock encoding that interleaves two clocks in the standard and Hadam…

A small and interesting architecture for early fault-tolerant quantum computers
Jacob S. Nelson, Andrew J. Landahl, Andrew D. Baczewski
https://arxiv.org/abs/2507.20387 https://…

A small and interesting architecture for early fault-tolerant quantum computers
We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in the X and Z bases, single- qubit Hadamard (H) gates, and three-qubit controlled-controlled-Z (CCZ) gates. State teleportations between [[4, 2, 2]] (2D) and [[8, 3, 2]] (3D) error-detecting color codes allow one to make use of the respective transversal H and …