Generators and relations for the group $U_4(\mathbb{Z}[1/\sqrt{2},i])$

Abstract

We give a presentation by generators and relations of the group $U_4(\mathbb{Z}[1/\sqrt{2},i])$ of unitary $4\times 4$ matrices with entries in the ring $\mathbb{Z}[1/\sqrt{2},i]$. This is motivated by the problem of exact synthesis for the Clifford+T gate set in quantum computation.

M.Sc. Thesis, Dalhousie University, 60 pages

References in corpus (2)

• Exact synthesis of multiqubit Clifford+T circuits
• Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates