基于全局二元辛形式简化的哈密顿模拟高效编译
Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification
AI总结：
本文提出基于二元辛形式的Symphony编译方法，在HamLib基准测试中使哈密顿模拟的两量子比特门数平均减59%、电路深度平均减91%，性能优于现有编译器。
AI中文摘要：
哈密顿模拟是核心量子工作负载，是变分量子算法和Trotter化时间演化的基础，这类程序表示为泡利指数序列，具有高度适合高层合成与优化的结构模式。然而，现有编译器即便采用先进的基于图或表的方法，也未能充分释放其全局代数结构的优化潜力。本文提出Symphony，一种基于泡利串的二元辛形式（BSF）表示的整体编译方法。与先前的分组BSF简化和基于路径的泡利网络综合不同，Symphony直接对全局BSF表应用广义受控泡利克利福德变换，自适应减少活跃泡利行，并在前向克利福德框架中发射符合条件的两量子比特块而非单量子比特旋转。代数简化后，Symphony执行保留因果性的块重调度启发式算法，该算法尊重框架诱导的依赖关系，同时暴露大量两量子比特块并行机会。这种精简的编译风格全面利用了同时的简化和可交换性机会，实现高效全局优化，无需依赖计算昂贵的启发式算法或长程搜索。在HamLib的通用哈密顿模拟基准测试中，Symphony实现两量子比特门数量平均减少59%，电路深度平均减少91%，严格帕累托优于现有最先进的编译器，所需两量子比特门数量减少1.14至1.58倍，尤其大幅将两量子比特电路深度平均缩小1.87至5.67倍。
英文摘要：
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, adaptively reducing active Pauli rows and emitting eligible two-qubit blocks other than 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 strictly Pareto-dominates prior state-of-the-art compilers, requiring 1.14--1.58$\times$ fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67$\times$ on average.
