二十面体群的量子散列
Quantum hashing with the icosahedral group
摘要：
我们研究了一种有效的算法，可以将任何单个量子比特门（或酉矩阵）散列成由二十面体群元素的乘积表示的Fibonacci任意子的辫子。通过用不同长度的辫段表示群元素，我们引入了一系列伪群。加入这些辫子段的重整化群的方式，我们得到一个高斯酉系综的随机矩阵表示的辫子。对于长度为O[log（1/）]的辫子，我们可以在时间上以O[log（1/）]的代价将所有SU（2）矩阵近似为平均误差。该算法适用于一般量子编译。
英文摘要：
We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudo-groups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O[log(1/epsilon)], we can approximate all SU(2) matrices to an average error epsilon with a cost of O[log(1/epsilon)] in time. The algorithm is applicable to generic quantum compiling.
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