Universal quantum circuit of near-trivial transformations

Any unitary transformation can be decomposed into a product of a group of near-trivial transformations. We investigate in detail the construction of universal quantum circuit of near trivial transformations. We first construct two universal quantum circuits which can implement any single-qubit rotation R-y(theta) and R-z(theta) within any given precision, and then we construct universal quantum circuit implementing any single-qubit transformation within any given precision. Finally, a universal quantum circuit implementing any n-qubit near-trivial transformation is constructed using the universal quantum circuits of R-y(theta) and R-z(theta). In the universal quantum circuit presented, each quantum transformation is encoded to a bit string which is used as ancillary inputs. The output of the circuit consists of the related bit string and the result of near-trivial transformation. Our result may be useful for the design of universal quantum computer in the future.