Generating Extensible High-Dimensional Entanglement via Two-Photon Qudit-Qudit Interactions

Quantum computing with D-level systems (or qudits) represents a promising alternative to traditional qubit based approaches by deploying a larger, and more connected Hilbert space for the same number of quantum units (in our case transmons). In our work, we explore extensible methods based on coherent two-photon XX-YY interactions in transmon qudits. These interactions realize relevant Hamiltonians for qudit based quantum simulation, allow subspace entangling interactions in larger coupled qudit architectures, and may enable high-dimensional quantum computing through improved circuit compilation. Specifically, we leverage these two-photon qudit-qudit interactions to experimentally demonstrate multi-controlled qubit Toffoli gates such as the CCZ and CCCZ gate, and also generate and tomographically reconstruct two-qudit Bell states up to D=4.