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The realization of robust universal quantum computation with any platformultimately requires both the coherent storage of quantum information and (atleast) one entangling operation between individual elements. The use ofcontinuous-variable bosonic modes as the quantum element is a promising routeto preserve the coherence of quantum information against naturally-occurringerrors. However, operations between bosonic modes can be challenging. Inanalogy to the exchange interaction between discrete-variable spin systems, theexponential-SWAP unitary [$\mathbf{U}_{\mathrm{E}}\left(\theta_c\right)$] cancoherently transfer the states between two bosonic modes, regardless of thechosen encoding, realizing a deterministic entangling operation for certain$\theta_c$. Here, we develop an efficient circuit to implement$\mathbf{U}_{\mathrm{E}}\left(\theta_c\right)$ and realize the operation in athree-dimensional circuit QED architecture. We demonstrate high-qualitydeterministic entanglement between two cavity modes with several differentencodings. Our results provide a crucial primitive necessary for universalquantum computation using bosonic modes.

Entangling Bosonic Modes via an Engineered Exchange Interaction