Quantum cellular automata are a coarse homology theory

2026/03/11 by Matthias Ludewig · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #math.KT #math-ph #math.GT #math.MG

paper · pdf

arxiv published 2026/03/11 · arxiv updated 2026/03/25

Abstract

We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectrum in the sense of algebraic topology is a direct consequence of the formal properties of coarse homology theories.

Citations

• Homotopy theory with bornological coarse spaces
• Index theory of one dimensional quantum walks and cellular automata
• Coarse homology theories

Discussions

• Matthias Ludewig: Quantum cellular automata are a coarse homology theory https://arxiv.org/abs/2603.10501 https://arxiv.org/pdf/2603.10501 https://arxiv.org/html/2603.10501 [bsky, 0 points, 0 comments]

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