Quantum Computing Forum

To implement an n-bit Toffoli gate, also known as the controlled-controlled-not (CCNOT) gate, you can use a combination of smaller Toffoli gates and single-qubit operations. The Toffoli gate performs a controlled-controlled-X operation, where the target qubit is flipped only if both control qubits are in the state |1⟩. Here's an example of how you can implement an n-bit Toffoli gate using smaller Toffoli gates:

Initialize your quantum circuit with n+2 qubits: n control qubits, 1 target qubit, and 1 ancillary qubit.

Apply Hadamard gates (H gate) to all n+2 qubits to create superposition:
Apply n Toffoli gates to create controlled-controlled-X operations. For each Toffoli gate, set the control qubits to the corresponding bits of your input, and set the target qubit to the ancillary qubit. The ancillary qubit acts as a temporary storage.
Apply a Toffoli gate to flip the target qubit if all control qubits are in the state |1⟩. Set the control qubits to the first n qubits, and set the target qubit to the ancillary qubit.
Apply the inverse of step 3 to restore the state of the ancillary qubit.
Apply the inverse of step 2 to restore the state of the qubits.
At this point, the n-bit Toffoli gate is implemented, and the final state of the qubits will depend on the inputs and whether the control qubits are all in the state |1⟩. Remember to measure the qubits of interest if you want to extract the results.

Note: This implementation assumes you are using a circuit model for quantum computation, such as the one used in quantum programming frameworks like Qiskit or Cirq. The code provided here is a Python-like pseudocode to illustrate the steps involved in implementing an n-bit Toffoli gate.