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PreprintCC BY 4.0arXiv

K-Theoretic Obstructions to Linearizing QCA Representations

  • Mattie Ji
  • Bowen Yang
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Abstract

Projective representations arise naturally in physics and representation theory, and determining whether they can be linearized has been a fundamental problem. In this work, we study the analogous problem for quantum cellular automata (QCA) representations, which incorporate locality constraints imposed by a metric space X. Over an arbitrary field 𝔽, we develop an obstruction theory for the linearization of QCA representations, using the algebraic K-theory spectrum of QCA constructed in previous work of the authors. The resulting obstructions are governed by the homotopy type of the QCA spaces, from which we extract universal obstruction classes to linearization. In the complex algebraic and unitary case, we also fully compute the homotopy types of the QCA spaces over a point, a line, and a plane.

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Cite

BibTeXRIS
BibTeX
@misc{ji2026ktheoretic,
  title = {{$K$-Theoretic Obstructions to Linearizing QCA Representations}},
  author = {Mattie Ji and Bowen Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.19657},
  eprint = {2606.19657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.19657},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - K-Theoretic Obstructions to Linearizing QCA Representations
AU  - Mattie Ji
AU  - Bowen Yang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2606.19657
UR  - https://arxiv.org/abs/2606.19657
AB  - Projective representations arise naturally in physics and representation theory, and determining whether they can be linearized has been a fundamental problem. In this work, we study the analogous problem for quantum cellular automata (QCA) representations, which incorporate locality constraints imposed by a metric space X. Over an arbitrary field 𝔽, we develop an obstruction theory for the linearization of QCA representations, using the algebraic K-theory spectrum of QCA constructed in previous work of the authors. The resulting obstructions are governed by the homotopy type of the QCA spaces, from which we extract universal obstruction classes to linearization. In the complex algebraic and unitary case, we also fully compute the homotopy types of the QCA spaces over a point, a line, and a plane.
ER  -