How can we code a ccz (control control z, equivalent of Toffoli on Z and not on X) gate in Qiskit language?

[quantumadmin]

The CCZ gate (Control-Control-Z gate) is a three-qubit gate that applies a phase factor of -1 to the target qubit if both control qubits are in the |1⟩ state. It is analogous to the Toffoli gate, which applies a NOT operation to the target qubit under the same conditions. In Qiskit, you can construct the CCZ gate using a combination of basic quantum gates.

Here's how you can code a CCZ gate in Qiskit:

Code: Select all

from qiskit import QuantumCircuit, Aer, execute

# Create a 3-qubit quantum circuit
qc = QuantumCircuit(3)

# Apply the CCZ gate
qc.cu1(np.pi, 0, 2)  # Controlled-Z gate between qubit 0 and qubit 2
qc.cx(1, 2)           # Controlled-X (CNOT) gate between qubit 1 and qubit 2
qc.cu1(-np.pi, 0, 2)  # Controlled-Z gate with a negative phase between qubit 0 and qubit 2
qc.cx(1, 2)           # Controlled-X (CNOT) gate between qubit 1 and qubit 2

# Simulate the circuit
simulator = Aer.get_backend('statevector_simulator')
job = execute(qc, simulator)
result = job.result()
statevector = result.get_statevector()

print("Final state vector:")
print(statevector)

In this example, the CCZ gate is constructed using a sequence of controlled-Z and controlled-X (CNOT) gates. The cu1 gate is used for the controlled-Z operations with the appropriate phase factors. The target qubit is qubit 2, and the control qubits are qubit 0 and qubit 1.

Please note that this is a simulation of the CCZ gate using a state vector simulator. On actual quantum hardware, the gate might be implemented using a different set of gates due to hardware constraints and gate decompositions.