6 papers
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…
CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs
A. Chervov, M. Obozov, A. Soibelman +31
This paper is the second in a series of studies on developing efficient artificial intelligence-based approaches to pathfinding on extremely large graphs (e.g. nodes) wit…
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…
Faster Algorithms for Structured Matrix Multiplication via Flip Graph Search
Kirill Khoruzhii, Patrick GelÃ, Sebastian Pokutta
We give explicit low-rank bilinear non-commutative schemes for multiplying structured matrices with , which serve as building blocks for recursive alg…
A Machine Learning Approach That Beats Large Rubik's Cubes
Alexander Chervov, Kirill Khoruzhii, Nikita Bukhal +9
The paper proposes a novel machine learning-based approach to the pathfinding problem on extremely large graphs. This method leverages diffusion distance estimation via a neural ne…