  Any unitary transformation can be decomposed into a product of a group of
near-trivial transformations. We investigate in details 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.
