Compile-once block encodings for masked similarity-transformed effective Hamiltonians

Bo Peng; Yuan Liu; Karol Kowalski

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arXiv · 2603.00761

Compile-once block encodings for masked similarity-transformed effective Hamiltonians

Bo Peng·Yuan Liu·Karol Kowalski

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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 and anti-Hermitian generators into rank-one bilinear and projected-quadratic ladders with near-linear scaling at fixed thresholds; each ladder admits deterministic, number-conserving preparation and a block encoding using constant number of signal ancillas. A fixed PREP-SELECT-PREP template multiplexes these ladders, and one QSP polynomial performs the spectral transformation with degree set by operator norms. For a fixed orbital pool and qubit register, the two-qubit fabric is compiled once; geometry, active-space (mask) updates, and truncations are absorbed by re-dialed single-qubit rotations. We introduce a mask-aware similarity-sandwich effective-Hamiltonian construction and benchmark stability under low-rank and second-order-perturation-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.

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Bo Peng, Yuan Liu, Karol Kowalski. 2026-02-28. Compile-once block encodings for masked similarity-transformed effective Hamiltonians. https://arxiv.org/abs/2603.00761

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