Simpler implementation of the Toffoli gate on IBM Q for special circumstances

[quantumadmin]

The Toffoli gate is a fundamental three-qubit gate in quantum computing that acts as a controlled-controlled-NOT gate (CCX gate). It flips the target qubit if both control qubits are in the |1⟩ state. However, the Toffoli gate requires a significant number of two-qubit gates, which can be challenging to implement on current quantum hardware due to noise and gate limitations.

In special circumstances where certain control qubits are in a specific state or where the Toffoli gate is required only for specific control configurations, you can simplify the implementation to reduce the number of gates and improve the gate fidelity. Here's an example of a simpler implementation of the Toffoli gate on IBM Q hardware for the specific case where one control qubit is in the |1⟩ state:

Code: Select all

from qiskit import QuantumCircuit, transpile, Aer, execute

# Initialize a quantum circuit
qc = QuantumCircuit(3)

# Apply a Toffoli gate using a single controlled-X (CX) gate
qc.cx(1, 2)  # Flips the target qubit if the second qubit is in the |1⟩ state

# Simulate the circuit
simulator = Aer.get_backend('qasm_simulator')
job = execute(qc, simulator)
result = job.result()
counts = result.get_counts()

print("Measurement outcomes:", counts)

In this example, the Toffoli gate is implemented using a single controlled-X (CX) gate. The first qubit is the control qubit, the second qubit is the second control qubit, and the third qubit is the target qubit. The controlled-X gate performs the NOT operation on the target qubit if the control qubit (in this case, qubit 1) is in the |1⟩ state.

Keep in mind that this simplified implementation of the Toffoli gate is limited to the specific case where one of the control qubits is in the |1⟩ state. For more general cases where both control qubits can be in arbitrary states, you would need to use the standard Toffoli gate implementation.

Additionally, when working with real quantum hardware, you should consider the error rates and gate limitations of the specific device you're using. Depending on the device characteristics, it might still be preferable to use a more robust implementation of the Toffoli gate, even if it requires more gates.