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Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates
by Po-Shen Hsin, Ryohei Kobayashi
Submission summary
| Authors (as registered SciPost users): | Po-Shen Hsin |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2511.15783v1 (pdf) |
| Date submitted: | Dec. 13, 2025, 11:56 p.m. |
| Submitted by: | Po-Shen Hsin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge theories induced by automorphisms of the gauge group, when the gauge theories have nontrivial topological actions in different spacetime dimensions. We discover the automorphism symmetry can be extended, become a higher group symmetry, and/or become a non-invertible symmetry. We illustrate the discussion with various models in field theory and on the lattice. In particular, we use automorphism symmetry to construct new transversal non-Clifford logical gates in topological quantum codes. In particular, we show that 2+1d $\mathbb{Z}_N$ qudit Clifford stabilizer models can implement non-Clifford transversal logical gate in the 4th level $\mathbb{Z}_N$ qudit Clifford hierarchy for $N\geq 3$, extending the generalized Bravyi-König bound proposed in the companion paper [arXiv:2511.02900] for qubits.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
2-The paper provides a wide range of concrete examples that clearly illustrate the core mechanisms. These include automorphism symmetries that are extended by gauged SPT defects, examples where defect fusion realizes higher-group structures, and examples where automorphisms give rise to non-invertible symmetries via a sandwich construction. Together, these examples convincingly demonstrate the generality of the framework.
3-The authors further apply their formalism to quantum error correction, showing how automorphism implementing logical gates in topological qudit codes. In particular, they present explicit constructions of logical gates in higher Clifford hierarchy for qudit stabilizer models, which goes beyond the standard qubit Bravyi–König bound.
Weaknesses
2-In the final section, the authors construct a logical gate lying in the fourth level of the Clifford hierarchy using their topological formalism. However, a concrete lattice-level implementation is not provided. Although such a circuit could in principle be derived from the underlying topological action, the absence of an explicit construction may limit accessibility for readers from the quantum information community.
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Requested changes
I would have two suggestions:
1-It would be beneficial for the authors to include a general discussion or comment on what kinds of generalized global symmetries (anyon permutations, logical operations) can be obtained within their framework starting from group automorphisms.
2-A more explicit discussion at the lattice and circuit level, including the role of boundary conditions, would be helpful for understanding how the proposed logical non-Clifford gate can be implemented in concrete topological codes.
Given the novelty of the results and their intrinsic theoretical interest, addressing these points may be considered optional and left to the authors’ discretion.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)