11 papers
On low-rank tensor train approximability for linear nearest neighbor systems
Patrick GelÃ, Sebastian Matera, Reinhold Schneider +1
Low-rank tensor methods are an important tool in the numerical treatment of equations with a high-dimensional state space. Nearest neighbor interaction systems like the Ising model…
The Weight Distribution of the Third-Order Reed-Muller Code of Length 2048
Kirill Khoruzhii, Patrick GelÃ, Sebastian Pokutta
We compute the weight distribution of the third-order Reed--Muller code RM(3,11) of length 2048. The weight enumerator is assembled from the coset weight enumerators of f+RM(2,10),…
Classification of Boolean Cubic Forms in Ten Variables
Kirill Khoruzhii, Patrick GelÃ, Sebastian Pokutta
We classify Boolean cubic forms in ten variables up to GL(10,2)-equivalence. The catalog contains all 3691560 nonzero orbits. For every orbit we provide a representative with small…
Graph Isomorphism: Mixed-Integer Convex Optimization from First-Order Methods
Wenjie Xiao, Mathieu Besançon, Patrick Gelà +3
The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be so…
Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Stefan Klus, Feliks Nüske, Patrick GelÃ
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspir…
Tensor Decomposition for Non-Clifford Gate Minimization
Kirill Khoruzhii, Patrick GelÃ, Sebastian Pokutta
Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While -count minimizat…