Author

R. Vilmart

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Preprint Sep 2026

Intuitionistic Unitary Linear Logic: A Proof-Theoretical Approach to Purely Quantum Higher-Order

Although the circuit model for quantum computation is well established, it is incapable of representing non-causal higher-order quantum processes such as the quantum switch. If several models of non-causal quantum computation have been considered in the literature, the approaches have so far only been focusing on the p...

Julien Lamiroy, Benoît Valiron, R. Vilmart · 0 citations

An Elementary Description of the Oracle of Efficient Sparse Matrices

This paper proposes an elementary description of a black-box function, and proposes an heuristic optimization for this description which minimizes implementation complexity using a clique cover technique, and proves the hardness of finding such an optimal solution under the optimization framework.

Benoît Valiron, R. Vilmart, AdhamZekri · 0 citations

Jul 2026

A Unique Normal Form for Tensor Trains over Arbitrary Fields

This work provides a unique normal form and associated polynomial-time reduction strategy for tensor trains over arbitrary fields, and crucially provides the first tensor train form with the uniqueness property.

R. Vilmart · arXiv.org · 0 citations