Quantum fourier transformation circuit and method of forming the same

An n-qubits Quantum Fourier Transform circuit that performs following steps (n is a natural number greater than or equal to 5),

• in a first step, applying a Hadamard gate to q0 qubit, applying an Rz(π/4) gate to the q1 qubit, applying an Rz(3π/2k+1) gate to qk qubits (k is a natural number greater than or equal to 5 and less than or equal to n−1);
• in a second step, applying a CNOT gate to the q0 gate, based on the qu qubit after the first step;
• in a third step, applying an Rz(−π/4) gate to the q0 qubit after the second step;
• in a fourth step, applying a CNOT gate to the q0 gate, based on the q1 qubit after the third step;
• in a fifth step, applying a Hadamard gate to the q1 qubit after the fourth step, and applying a CNOT gate to a third ancilla qubit |0>, based on the q4 qubits after the first step;
• in a sixth step, applying a CNOT gate to a second ancilla qubit |0>, based on the q3 qubit after the first step;
• in a seventh step, applying a CNOT gate to a first ancilla qubit |0>, based on the q2 qubits after the first step;
• in an eighth step, applying a CNOT gate to the first to third ancilla qubits, based on the q1 qubit after the fifth step;
• in a ninth step, applying a CNOT gate to q2 to qu qubits, based on the q0 qubits after the fourth step;
• in a tenth step, applying an Rz(−π/8) gate to the q2 qubit, applying an Rz(−π/16) gate to the q3 qubit, applying an Rz(−π/32) gate to the q4 qubit, applying an Rz(−π/4) gate to the first ancilla qubit, applying an Rz(−π/8) gate to the second ancilla qubit, and applying an Rz(−π/16) gate to the third ancilla qubit;
• in an eleventh step, applying a CNOT gate to the q2, q3, and q4 qubits, based on the q0 qubit;
• in a twelfth step, applying a CNOT gate to the first to third ancilla qubits, based on the q1 qubit;
• in a thirteenth step, applying a CNOT gate to the first ancilla qubit, based on the q2 qubit;
• in a fourteenth step, applying a CNOT gate to the second ancilla qubit, based on the q3 qubit;
• in a fifteenth step, applying a CNOT gate to the third ancilla qubit, based on the q4 qubit;
• in a sixteenth step, applying a Hadamard gate to the q2 qubit;
• in a seventeenth step, applying a CNOT gate to the q2 qubit, based on the q3 qubit;
• in an eighteenth step, applying an Rz(−π/4) gate to the q2 qubit;
• in a nineteenth step, applying a CNOT gate to the q2 qubit, based on the q3 qubit;
• in a twentieth step, applying a Hadamard gate to the q3 qubit;
• in a twenty first step, applying a CNOT gate to the first ancilla qubit, based on the q4 qubit;
• in a twenty second step, applying a CNOT gate to the first ancilla qubit, based on the q3 qubit;
• in a twenty third step, applying a CNOT gate to the q4 qubit, based on the q2 qubit;
• in a twenty fourth step, applying an Rz(−π/8) gate to the q4 qubit, and applying an Rz(−π/4) gate to the first ancilla qubit;
• in a twenty fifth step, applying a CNOT gate to the q4 qubit, based on the q2 qubit;
• in a twenty sixth step, applying a CNOT gate to the first ancilla qubit, based on the q3 qubit;
• in a twenty seventh step, applying a CNOT gate to the first ancilla qubit, based on the q4 qubit;
• in a twenty eighth step, applying an Rz(15π/32) gate to the q0 qubit, applying an Rz(7π/16) gate to the q1 qubit, applying an Rz(3π/8) gate to the q2 qubit, applying an Rz(π/4) gate to the q3 qubit, and applying a Hadamard gate to the q4 qubit;
• in a twenty ninth step, swapping the q1 qubit and the q3 qubit;
• and
• in a thirtieth step, swapping q0 and q4 qubits, wherein
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