The Group of Dyadic Unitary Matrices
Alexis De Vos, Raphaël Van Laer, Steven Vandenbrande · Open Systems & Information Dynamics · 2012
We introduce the group DU (m) of m × m dyadic unitary matrices, i.e. unitary matrices with all entries having a real and an imaginary part that are both rational numbers with denominator of the form 2p(with p a non-negative integer). We investigate in detail the finite groups DU(1) and DU(2) and the discrete, but infinite groups DU(3) and DU(4). We further introduce the subgroup XDU (m) of DU (m), consisting of those members of DU (m) that have constant line sum 1. The study of XDU(2) and XDU(4) leads to conclusions concerning the synthesis of quantum computers acting on one and two qubits, respectively.