Quantum Computing with the Subgroup YU(n) of the Unitary Group U(n)

Starting from the three Pauli matrices, it is possible to construct a synthesis procedure for an arbitrary quantum circuit. A prominent role is played by X-circuits and Y-circuits. They constitute the [Formula: see text]-dimensional subgroups XU([Formula: see text]) and YU([Formula: see text]) of the [Formula: see text]-dimensional group U([Formula: see text]). The former are described by unitary matrices with all line sums equal to 1. The latter are described by unitary matrices with all weighted line sums equal to 1. Whereas the group XU([Formula: see text]) has been studied before, investigation of the group YU([Formula: see text]) is new.