Quantum logical controlled-NOT gate in a lithium niobate-on-insulator photonic quantum walk

The two-qubit controlled-NOT gate is one of the central entangling operations in quantum information technology. The controlled-NOT gate for single photon qubits is normally realized as a network of five individual beamsplitters on six optical modes. Quantum walks (QWs) are an alternative photonic architecture involving arrays of coupled waveguides, which have been successful for investigating condensed matter physics, however, have not yet been applied to quantum logical operations. Here, we engineer the tight-binding Hamiltonian of an array of lithium niobate-on-insulator waveguides to experimentally demonstrate the two-qubit controlled-NOT gate in a QW. We measure the two-qubit transfer matrix with 0.938 +/- 0.003 fidelity, and we use the gate to generate entangled qubits with 0.945 +/- 0.002 fidelity by preparing the control photon in a superposition state. Our results highlight a new application for QWs that use a compact multi-mode interaction region to realize large multi-component quantum circuits.