How would one implement a 4-qubit CCCNOT gate (equivalent to controlled-Toffoli)?

[quantumadmin]

A 4-qubit CCCNOT gate, also known as the controlled-Toffoli gate, is an extension of the Toffoli gate (controlled-controlled-NOT gate) that acts on three control qubits and one target qubit. It applies a NOT (X) operation to the target qubit if all three control qubits are in the |1⟩ state. Here's how you can implement a 4-qubit CCCNOT gate using a quantum circuit composed of basic quantum gates.

In this explanation, We will use Qiskit, a popular Python library for working with quantum circuits. Make sure you have Qiskit installed (pip install qiskit).

Code: Select all

from qiskit import QuantumCircuit, transpile, assemble, Aer, execute
from qiskit.visualization import plot_bloch_multivector, plot_histogram

# Create a 4-qubit quantum circuit
qc = QuantumCircuit(4)

# Apply the CCCNOT gate (controlled-Toffoli)
qc.ccx(0, 1, 3)  # First two qubits are control qubits, last qubit is the target

# Visualize the circuit
print(qc)

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

# Print the final state vector
print("Final state vector:")
print(statevector)

In this example, we create a 4-qubit quantum circuit using Qiskit's QuantumCircuit class. We then apply the ccx gate (controlled-Toffoli gate) to the qubits. The first two qubits are control qubits, and the last qubit is the target qubit.

Note that the ccx gate is a built-in gate in Qiskit that performs the controlled-Toffoli operation. If you're implementing this gate on actual quantum hardware, the underlying operations might be different due to the specific gate set supported by the hardware.

Remember that this is a simulation of the quantum circuit using a state vector simulator. In a real quantum computer, the gates might be implemented using a different set of operations or approximations.