Quantum cellular automata are a coarse homology theory
Matthias Ludewig
TL;DR
This paper demonstrates that quantum cellular automata (QCA) can be understood as part of a coarse homology theory, linking quantum computation models with algebraic topology concepts.
Contribution
It establishes that QCA form the degree-zero component of a coarse homology theory, connecting recent topological results to formal properties of coarse homology.
Findings
QCA form the degree-zero part of a coarse homology theory
Recent results on QCA as an Omega-spectrum follow from coarse homology properties
Provides a topological framework for understanding quantum cellular automata
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research