Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations

Naihong Hu; Futao Wang

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arXiv · 2608.31011

Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations

Naihong Hu·Futao Wang

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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.

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Naihong Hu, Futao Wang. 2026-08-31. Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations. https://arxiv.org/abs/2608.31011

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