This paper introduces Genesis, the first compiler designed to support<br>Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable<br>(DV) quantum computing systems. Genesis is a two-level compilation system. At<br>the first level, it decomposes an input Hamiltonian into basis gates using the<br>native instruction set of the target hybrid CV-DV quantum computer. At the<br>second level, it tackles the mapping and routing of qumodes/qubits to implement<br>long-range interactions for the gates decomposed from the first level. Rather<br>than a typical implementation that relies on SWAP primitives similar to<br>qubit-based (or DV-only) systems, we propose an integrated design of<br>connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for<br>hybrid CV-DV systems. We also introduce an OpenQASM-like domain-specific<br>language (DSL) named CVDV-QASM to represent Hamiltonian in terms of<br>Pauli-exponentials and basic gate sequences from the hybrid CV-DV gate set.<br>Genesis has successfully compiled several important Hamiltonians, including the<br>Bose-Hubbard model, $\mathbb{Z}_2-$Higgs model, Hubbard-Holstein model,<br>Heisenberg model and Electron-vibration coupling Hamiltonians, which are<br>critical in domains like quantum field theory, condensed matter physics, and<br>quantum chemistry. Our implementation is available at<br>Genesis-CVDV-Compiler(https://github.com/ruadapt/Genesis-CVDV-Compiler).