Compile‐Once Block Encodings for Masked Similarity‐Transformed Effective Hamiltonians

ABSTRACT We present COMPOSER, a compile‐once modular parametric oracle for similarity‐encoded effective reduction of electronic‐structure operators (e.g., Schrieffer–Wolff‐type constructions). Low‐rank factorizations compress Hamiltonians into empirically near‐linear ladder pools at fixed factorization thresholds, and represent anti‐Hermitian generators through threshold‐controlled bilinear, decomposable‐pair, or generic elementary‐excitation branch libraries; each declared primitive branch admits a number‐conserving Fock‐space block encoding, with coefficient‐space dyads understood through their number‐conserving second‐quantized lifts. A fixed PREP‐SELECT‐PREP template multiplexes these branches, and a standard block‐Hamiltonian simulation/QSP primitive exponentiates the Hermitian generator with degree or query complexity set by operator norms and the chosen error tolerance. For a fixed orbital pool, qubit register, branch‐primitive library, selector address map, ancilla layout, routing plan, maximum branch set, and global normalization, the two‐qubit fabric is compiled once; geometry, active‐space (mask) updates, and truncations are absorbed by updated numerical weights, rotation angles, and classical masks. We introduce a mask‐aware similarity‐sandwich effective‐Hamiltonian construction and benchmark stability under low‐rank and second‐order‐perturbation‐guided screening. COMPOSER is an execution architecture: algorithmic errors (block‐encoding and QSP approximation) are tunable for any supplied parameters, while physical accuracy depends on how those parameters are obtained if not refined.