Preparation of Quantum Superposition Using Partial Negation

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 is proposed to prepare a quantum superposition from a given space of probability distributions. The speed of the preparation process and the accuracy of the prepared superposition has special importance to the success of any quantum algorithm. The proposed method can be used to prepare the required quantum superposition in $\mathscr {O}(n)$ steps and with high accuracy when compared with relevant methods in literature.