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Quantum Circuit Design Gate Engineering

Multiary gradings

arXiv
Authors: Steven Duplij

Year

2026

Paper ID

3692

Status

Preprint

Abstract Read

~2 min

Abstract Words

95

Citations

N/A

Abstract

This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various compatibility conditions between the arity of algebra operations and grading group operations. Key results include quantization rules connecting arities, classification of graded homomorphisms, and concrete examples including ternary superalgebras and polynomial algebras over n-ary matrices. The theory reveals fundamentally new phenomena not present in the binary case, such as the existence of higher power gradings and nontrivial constraints on arity compatibility.

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  • This paper contributes to the Quantum Circuit Design & Gate Engineering research area in the Quantum Articles archive.
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  • This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.11738 [2] arXiv https://arxiv.org/abs/2601.11738 [3] Publisher https://arxiv.org/abs/2601.11738

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