Pith. sign in

REVIEW 3 cited by

An index for quantum cellular automata on fusion spin chains

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2309.10961 v2 pith:IEXCFWVZ submitted 2023-09-19 math.OA math-phmath.MPmath.QAquant-ph

Corey Jones , Junhwi Lim This is my paper · ORCID
classification math.OAmath-phmath.MPmath.QAquant-ph
keywords indexchainsfusionspinautomatacellularinvariantoperators
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

Interpreting the GNVW index for 1D quantum cellular automata (QCA) in terms of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators of 2D topological codes. We show that for the fusion spin chains built from the fusion category $\mathbf{Fib}$, the index is a complete invariant for the group of QCA modulo finite depth circuits.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Causal Decompositions of 1D Quantum Cellular Automata

    quant-ph 2025-06 conditional novelty 8.0 of 10

    For N > 4r, every 1D quantum cellular automaton of causality radius r is exactly a routed unitary circuit of nearest-neighbour interactions, and translation-invariant automata get translation-invariant circuits.

  2. Quantum Cellular Automata on Symmetric Subalgebras

    quant-ph 2024-11 conditional novelty 8.0 of 10

    Quantum cellular automata on finite-Abelian-symmetric subalgebras of 1D spin chains are completely classified by an anyon-permutation invariant and a generalized GNVW index.

  3. Non-invertible SPTs: an on-site realization of (1+1)d anomaly-free fusion category symmetry

    cond-mat.str-el 2024-12 conditional novelty 6.0 of 10

    Anomaly-free fusion category symmetries have a canonical trivial phase, and the three Rep†(D8) symmetry-protected topological phases are explicitly realized by Q-system lattice models connected by an S3 duality.

Pith tools