Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations

Abstract:Fault-tolerant quantum computation requires robust protection of encoded quantum information. In this work, we develop a representation-theoretic framework for constructing protected logical qudits in finite-group Kitaev quantum double models. By introducing $\varepsilon$-stable irreducible representations, we establish a necessary and sufficient existence criterion and derive ribbon--projector commutation relations that yield a $d$-dimensional protected logical subspace. We apply this construction to symmetric and alternating groups, obtaining logical qubits for $S_n$ ($n\ge 3$) and a logical qutrit for $A_4$. Moreover, the family $(\mathbb Z_2)^d\rtimes\mathbb Z_d$ realizes protected logical qudits of arbitrary dimension $d\ge 2$. Finally, for $D(A_4)$, we describe a scheme for universal logical qutrit computation using ribbon-based logical operations.

Quantum Physics (quant-ph); Representation Theory (math.RT)

arXiv:2608.31011 [quant-ph]

(or arXiv:2608.31011v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.31011 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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