International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste, Italy.
Phys Rev Lett. 2010 Apr 23;104(16):160502. doi: 10.1103/PhysRevLett.104.160502.
We study an efficient algorithm to hash any single-qubit gate 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 pseudogroups. 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(log2(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.
我们研究了一种高效的算法,可将任意单量子比特门哈希成由二十面体群元素的乘积表示的 Fibonacci 任意子的纽结。通过将群元素表示为不同长度的纽结片段,我们引入了一系列伪群。以重整化群的方式连接这些纽结片段,我们得到了一个随机矩阵表示的纽结的高斯幺正系综。对于长度为 O(log2(1/epsilon))的纽结,我们可以以 O(log(1/epsilon))的时间复杂度将所有 SU(2)矩阵平均误差为 epsilon 的方式进行近似。该算法适用于通用量子编译。