  The preparation of a quantum superposition is the key to the success of many
quantum algorithms and quantum machine learning techniques. The preparation of
an incomplete or a non-uniform quantum superposition with certain properties is
a non-trivial task. In this paper, an $n$-qubits variational quantum circuit
using partial negation and controlled partial negation operators will be
proposed to prepare an arbitrary quantum superposition. The proposed quantum
circuit follows the symmetries of the unitary Lie group. The speed of the
preparation process and the accuracy of the prepared superposition has a
special importance to the success of any quantum algorithm. The proposed method
can be used to prepare the required quantum superposition in $\mathcal{O}(n)$
steps and with high accuracy when compared with relevant methods in literature.

Quantum Physics