Universal construction of unitary transformation of quantum computation with one- and two-body interactions

Abstract

Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary representation in usual computational basis. This decomposition may be simplified greatly with the help of the properties of the finite-dimensional multiple-quantum operator algebra spaces of a quantum system and the specific properties of a given quantum algorithm. As elementary building blocks of quantum computation, the two-qubit diagonal gates and one-qubit gates may be constructed physically with one- and two-body interactions in a two-state quantum system and hence could be conveniently realized experimentally. The present work will be helpful for implementing generally any N-qubit quantum computation in those feasible two-state quantum systems and determining conveniently the time evolution of these systems in course of quantum computation.