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quant-ph2026
Minimality of the Pure Qubit ZX Calculus
Harry K. Stoltz, Renaud Vilmart
The ZX calculus is a graphical language for reasoning about quantum processes. In this paper, we develop a minimal pure-qubit ZX calculus based on the work of Vilmart [arXiv:1812.0…
cs.LO2026
Intuitionistic Unitary Linear Logic: A Proof-Theoretical Approach to Purely Quantum Higher-Order
Julien Lamiroy, Benoît Valiron, Renaud Vilmart
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 sev…
cs.DS2026
A Unique Normal Form for Tensor Trains over Arbitrary Fields
Renaud Vilmart
Tensor trains (or Matrix-Product States) are a data structure used in many fields of computer science and physics. They were recently shown to generalise binary decision diagrams w…