Generators and Relations for Un(Z[1/2,i])
Quantum Physics
2021-09-14 v2 Emerging Technologies
Logic in Computer Science
Abstract
Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, omega^dagger H, 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 nxn-matrices with entries in Z[1/2,i].
Cite
@article{arxiv.2105.14047,
title = {Generators and Relations for Un(Z[1/2,i])},
author = {Xiaoning Bian and Peter Selinger},
journal= {arXiv preprint arXiv:2105.14047},
year = {2021}
}
Comments
In Proceedings QPL 2021, arXiv:2109.04886