Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification
Abstract
Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods. We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, progressively reducing active Pauli rows while adaptively emitting eligible two-qubit blocks in addition to single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It Pareto-dominates prior state-of-the-art compilers, requiring 1.17--1.58× fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67× on average.
Related
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BibTeX
@misc{yang2026efficient,
title = {{Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification}},
author = {Zhaohui Yang and Yuwei Han and Ruiyun Zhang and Dawei Ding and Jianxin Chen and Yuan Feng and Yuan Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.11579},
eprint = {2608.11579},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11579},
}
RIS
TY - UNPB
TI - Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification
AU - Zhaohui Yang
AU - Yuwei Han
AU - Ruiyun Zhang
AU - Dawei Ding
AU - Jianxin Chen
AU - Yuan Feng
AU - Yuan Xie
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2608.11579
UR - https://arxiv.org/abs/2608.11579
AB - Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods. We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, progressively reducing active Pauli rows while adaptively emitting eligible two-qubit blocks in addition to single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It Pareto-dominates prior state-of-the-art compilers, requiring 1.17--1.58× fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67× on average.
ER -