The multiplier based on quantum Fourier transform

In the paper, we first present a quantum multiplier based on quantum Fourier transform (QFT), which is composed by a series of double-controlled phase gates, the control qubits are from the two multipliers, and the controlled qubits are in the ancillary state. By the sequential usage of the double-controlled phase gates, the product could be obtained after the inverse quantum Fourier transform (IQFT) on the final ancillary output state. Then, we further optimize the proposed quantum multiplier. The circuit analysis shows that the proposed multiplier could reduce the number of qubits in ancillary, and the multiplication result of finite qubits can be directly obtained by using fewer quantum gates. The optimization has reduced the resource cost of quantum multiplier greatly.