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

TL;DR

COMPOSER is a modular quantum algorithm framework that efficiently encodes and transforms electronic-structure Hamiltonians using low-rank factorizations, enabling scalable and adaptable quantum simulations.

Contribution

It introduces a compile-once, modular approach for similarity-encoded Hamiltonians with low-rank factorizations and a flexible execution architecture for quantum chemistry simulations.

Findings

Near-linear scaling of Hamiltonian compression

Deterministic, number-conserving state preparation

Stable benchmarking under low-rank screening

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.