Quantum circuit for implementing a multi-controlled not gate

A quantum circuit for implementing multi-controlled NOT gates with N control qubits, where N is an integer greater than or equal to 3, the quantum circuit comprising:

• a first auxiliary circuit corresponding to one or more initial layers in the plurality of layers and configured to perform controlled NOT operation on a target qubit based on an Nth control qubit from among the N control qubits and a first auxiliary qubit initialized to a |+> state in the plurality of auxiliary qubits;
• a quantum gate group corresponding to a plurality of layers and configured to perform controlled NOT operation on the first auxiliary qubit based on first to (N−1)th control qubits;
• and
• a measurement area corresponding to a last one or more layers of the plurality of layers and including one or more measurement circuits that measure a state of one or more auxiliary qubits, and one or more conditional operation circuits that perform a conditional operation based on a measurement result of the one or more measurement circuits.

A quantum circuit comprising:

• corresponding to a first layer, a first H gate configured to perform Hadamard transformation on a target qubit, and a second H gate configured to perform Hadamard transformation on a first auxiliary qubit initialized to the |0> state;
• corresponding to a second layer, a first CNOT gate and configured to rotate a second control qubit by π about X axis based on the first auxiliary qubit;
• corresponding to a third layer, a second CNOT gate and configured to rotate a third control qubit by π about the X-axis based on a first control qubit, and a third CNOT gate configured to rotate a second auxiliary qubit initialized to a |0> state by π about the X axis based on the target qubit;
• corresponding to a fourth layer, a fourth CNOT gate configured to rotate the third control qubit by π about the X axis based on the first auxiliary qubit;
• corresponding to a fifth layer, a fifth CNOT gate configured to rotate the second auxiliary qubit by π about the X axis based on the first control qubit;
• corresponding to a sixth layer, a sixth CNOT gate configured to rotate the first control qubit by π about the X axis based on the second control qubit, a seventh CNOT gate configured to rotate the target qubit by π about the X axis based on the third control qubit, and an eighth CNOT gate configured to rotate the second auxiliary qubit by π based on the first auxiliary qubit;
• corresponding to a seventh layer, a first T gate configured to perform π/4 phase transformation on the first control qubit, a first inverse T gate configured to perform −π/4 phase transformation on the second control qubit, a second inverse T gate configured to perform −π/4 phase transformation on the third control qubit, a second T gate configured to perform the π/4 phase transformation on the target qubit, a third T gate configured to perform π/4 phase transformation on the first auxiliary qubit, and a third inverse T gate configured to perform −π/4 phase transformation on the second auxiliary qubit;
• corresponding to an eighth layer, a ninth CNOT gate configured to rotate the first control qubit by π about the X axis based on the second control qubit, a tenth CNOT gate configured to rotate the target qubit by the x about the X axis based on the third control qubit, and an eleventh CNOT gate configured to rotate the second auxiliary qubit by π about the X axis based on the first auxiliary qubit;
• corresponding to a ninth layer, a twelfth CNOT gate configured to rotate the second auxiliary qubit by π about the X axis based on the first control qubit;
• corresponding to a tenth layer, a thirteenth CNOT gate configured to rotate the third control qubit by π about the X axis based on the first auxiliary qubit;
• corresponding to an eleventh layer;
• a fourteenth CNOT gate configured to rotate the third control qubit by π about an X axis based on the first control qubit, and a fifteenth CNOT gate configured to rotate the second auxiliary qubit by π about the X axis based on the target qubit;
• corresponding to a twelfth layer, a sixteenth CNOT gate configured to rotate the second control qubit by π about the X axis based on the first auxiliary qubit;
• corresponding to a thirteenth layer, a seventeenth CNOT gate configured to rotate the first auxiliary qubit by π about the X axis based on the first control qubit;
• corresponding to a fourteenth layer, a third H gate configured to perform Hadamard transformation on the target qubit, and a first inverse V gate configured to rotate the first auxiliary qubit by −π/2 about the X axis;
• corresponding to a fifteenth layer a first measurement circuit configured to measure the first auxiliary qubit on Z basis;
• corresponding to a sixteenth layer, a first inverted conditional operation circuit configured to not perform an operation in response to a measurement result being 1, and to rotate the target qubit by π about the X axis based on the third control qubit in response to the measurement result being 0;
• and
• corresponding to a seventeenth layer, a first conditional operation circuit configured to do not perform an operation in response to the measurement being 0, and to rotate the second control qubit by π about Z axis based on the first control qubit in response to the measurement result being 1.