Quantum circuits on resource-limited hardware require optimizing regions dominated by $\{\mathrm{CNOT}, R_z\}$, which account for a large fraction of operations and often dominate execution cost. This optimization can be challenging because phase-polynomial blocks are fragmented by basis-changing gates such as $H$, and optimizing phase parities alone may increase the cost of downstream basis transformations. Existing phase-polynomial approaches are limited to single-block or phase-only optimization, while subcircuit rewriting approaches are local and scale poorly beyond small rewrite windows. We introduce \emph{PhasePoly}, a compiler optimization pass that jointly optimizes phase-parity and output-parity networks and employs a cross-block intermediate representation to reuse parities across phase-polynomial block barriers. This approach is effective because its unified parity-matrix representation exposes long-range $\{\mathrm{CNOT}, R_z\}$ structure that local rewriting and single-block methods cannot capture. \emph{PhasePoly} reduces total gate count by up to 50.00\% (34.70\% on average) and CNOT count by up to 48.57\% (26.83\% on average), while scaling to large circuits and improving both fault-tolerant compilation and near-term hardware execution. \emph{PhasePoly} is available at https://github.com/ruadapt/PhasePoly.

This paper introduces Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems.Genesis is a two-level compilation system.At the first level, it decomposes an input Hamiltonian into basis gates using the native instruction set of the target hybrid CV-DV quantum computer.At the second level, it tackles the mapping and routing of qumodes/qubits to implement long-range interactions for the gates decomposed from the first level.Rather than a typical implementation that relies on SWAP primitives similar to qubit-based (or DV-only) systems, we propose an integrated design of connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for hybrid CV-DV systems.We also introduce an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CV-DV gate set.Genesis has successfully compiled several important Hamiltonians, including the Bose-Hubbard model, Z 2 -Higgs model, Hubbard-Holstein model, Heisenberg model and Electron-vibration coupling Hamiltonians, which are critical in domains like quantum field theory, condensed matter physics, and quantum chemistry.Our implementation is available at Genesis-CVDV-Compiler https://