Generators and Relations for Un(Z[1/2; i])

被引：2

作者：

Bian, Xiaoning ^{[1
]}

Selinger, Peter ^{[1
]}

机构：

[1] Dalhousie Univ, Halifax, NS, Canada

来源：

ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE | 2021年 / 343期

关键词：

D O I：

10.4204/EPTCS.343.8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, omega H-dagger, and S. All of these gates have matrix entries in the ring Z[1/2, i], the smallest subring of the complex numbers containing 1/2 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in Z[1/2, i] can be realized by a quantum circuit over the above gate set using at most one ancilla. In this paper, we give a finite presentation by generators and relations of U-n(Z[1/2, i]), the group of unitary n x n-matrices with entries in Z[1/2, i]

引用

页码：145 / 164

页数：20

共 12 条

[1] Number-Theoretic Characterizations of Some Restricted Clifford [J].