Implementation of Toffoli gates with a single asymmetric Heisenberg XY interaction

The Toffoli gate, which has practical applications in the implementation of practical quantum algorithms and quantum error correction, is usually constructed from concatenated two-qubit or qubit-qutrit gates. Here we show that the Toffoli gate for three qubits can be implemented through a single XY interaction plus two single-qubit rotations. This method greatly simplifies the experimental implementation of the Toffoli gate and promises a much higher fidelity compared to those based on elementary gate decomposition. We present an example for the implementation of the required XY interaction in cavity QED. DOI: 10.1103/PhysRevA.87.042318