基于稳定表示的Kitaev量子双重模型中的受保护逻辑量子位
Protected Logical Qudits in Kitaev Quantum Double Models via Stable Representations
AI总结：
本研究在Kitaev量子双重模型中引入ε-稳定不可约表示，构建受保护逻辑量子位的表示论框架，实现特定群的逻辑量子位及通用qutrit计算方案。
AI中文摘要：
容错量子计算需要对编码量子信息进行可靠保护。本研究构建有限群Kitaev量子双重模型中受保护逻辑量子位的表示论框架，引入ε-稳定不可约表示，建立存在性的充要判据，推导带投影子交换关系，得到d维受保护逻辑子空间。将该构造应用于对称群与交错群，得到Sₙ（n≥3）的逻辑量子位、A₄的逻辑qutrit；(ℤ₂)ᵈ⋊ℤ_d族实现任意维度d≥2的受保护逻辑量子位；针对D(A₄)，提出基于带操作的通用逻辑qutrit计算方案。
英文摘要：
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.
