Polarization and Orbital Angular Momentum Encoded Quantum Toffoli Gate Enabled by Diffractive Neural Networks

Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive to performing complex quantum algorithms. Here, we propose and present an experimental demonstration of a quantum Toffoli gate fully exploiting the polarization and orbital angular momentum of a single photon. The Toffoli gate is implemented using the polarized diffractive neural networks scheme, achieving a mean truth table visibility of 97.27±0.20%. We characterize the gate's performance through quantum state tomography on 216 different input states and quantum process tomography, which yields a process fidelity of 94.05±0.02%. Our method offers a novel approach for realizing the Toffoli gate without requiring exponential optical elements while maintaining extensibility to the implementation of other three-qubit gates.