Higher-order circuits
Quantum Physics
2026-02-24 v1 Logic in Computer Science
Category Theory
Abstract
We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order bipartite processes and higher-order bipartite states. In category-theoretic terms, these laws are expressed using enrichment and cotensors in symmetric polycategories, along with a frobenius-like coherence between them. We describe how these laws capture the salient features of higher-order quantum theory, and discover an upper bound for higher-order circuits: any higher-order circuit theory embeds into the theory of strong profunctors.
Keywords
Cite
@article{arxiv.2602.18701,
title = {Higher-order circuits},
author = {Matt Wilson},
journal= {arXiv preprint arXiv:2602.18701},
year = {2026}
}