AI 中文总结
该研究提出一种自适应多后端模拟器，结合平衡量子比特二分划分的费曼路径求和与稳定器框架模拟，通过成本模型优化划分，在结构化基准测试中大幅优于现有模拟器，且具有良好的并行性。
AI 中文摘要
我们提出了一种针对克利福德+T量子电路的精确振幅模拟器，该模拟器将平衡量子比特二分划分的费曼路径求和与每一半的稳定器框架模拟相结合。该构造在三个方向上扩展了现有的基于稳定器的薛定谔-费曼方法：递归多级二分划分形成二叉树；当叶节点的稳定器框架超出其内存上限时，自动回退到密集状态矢量模拟；以及采用成本模型驱动的划分选择器，替代标准的割计数最小化启发式方法。我们表明，割计数最小化在实践中是不可靠的替代方案：全局更优的划分可能会减少跨割数量，但会增加墙钟时间，因为它会使两半的T门密度失衡，并增大每一半的稳定器框架规模。我们的成本模型将每一侧的密集2n上限替换为稳定器框架上限2w，并显式建模每个振幅的读出成本；分离该项后，我们发现叶节点模拟器路径末端振幅提取存在二次渐近低效问题，通过将其替换为现有的O(F * s * n)单振幅内积解决了该问题。在结构化分层n=16基准测试中，递归模拟器比整体稳定器框架模拟快92倍至17645倍；在相同割条件下，与密集半状态矢量基线相比，每条路径快79倍；端到端比生产级状态矢量模拟器快高达47.9倍（中位数约5倍）。在对抗性随机克利福德+T电路上，密集状态矢量在跨割门数接近n/2的交叉点后胜出——这是成本模型识别的区域。主要成本来自跨割费曼求和，其具有可高度并行性且工作进程间通信恒定，不同于近期的矩阵乘积态稳定器-张量方法，后者的内部收缩循环是顺序执行的。
英文摘要
We present an exact amplitude simulator for Clifford+T quantum circuits that combines a Feynman path sum across a balanced qubit bipartition with stabilizer-frame simulation on each half. The construction extends prior stabilizer-based Schrödinger-Feynman methods in three directions: recursive multilevel bipartition into a binary tree, automatic fallback to dense state-vector simulation when a leaf's stabilizer frame would exceed its memory ceiling, and a cost-model-driven partition selector that replaces the standard cut-count minimization heuristic. We show cut-count minimization is an unreliable proxy in practice: a globally cleaner partition can reduce cross-cut count yet increase wall-clock time, because it imbalances T-gate density across halves and inflates per-half stabilizer-frame size. Our cost model substitutes the stabilizer-frame bound 2w for the dense 2n ceiling per side and explicitly models per-amplitude readout cost; isolating that term uncovered a quadratic-asymptotic inefficiency in the leaf simulator's end-of-path amplitude extraction, fixed by replacing it with an existing O(F * s * n) single-amplitude inner product. On a structured hierarchical n=16 benchmark the recursive simulator beats monolithic stabilizer-frame simulation by 92x to 17,645x, wins by 79x per path against a dense half-state-vector baseline under an identical cut, and beats a production state-vector simulator end to end by up to 47.9x (median ~5x). On adversarial random Clifford+T circuits the dense state vector wins past a crossover near n/2 cross-cut gates -- the regime the cost model identifies. The dominant cost, the cross-cut Feynman sum, is embarrassingly parallel with constant inter-worker communication, unlike recent matrix-product-state stabilizer-tensor methods whose inner contraction loop is sequential.
Comments35 pages, 2 appendices, 3 figures, 7 tables
