论文标题
超对称旋转链的拓扑量子计算
Topological Quantum Computation on Supersymmetric Spin Chains
论文作者
论文摘要
由编织组元素构建的量子门构成了拓扑量子计算的构件。他们已经在$ su（2）_k $ Quantum Group理论中进行了广泛的研究，这是非亚伯里亚人（例如Ising（$ k = 2 $），fibonacci（$ k = 3 $）和Jones-Kauffman（$ K = 4 $）的丰富示例。我们表明，这些非元系统的融合空间可以精确映射到某些类似尼古拉的超对称旋转链的乘积状态零模式。结果，我们可以在这些超对称系统的产品状态零模式下实现辫子组。这些操作员在希尔伯特空间中杀死了所有其他状态，从而在处理信息时阻止了错误的发生，从而适合于量子计算。
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising ($k=2$), Fibonacci ($k=3$) and Jones-Kauffman ($k=4$) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group on the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing.
