发表机构
University of Antwerp; Technical University Delft; TU Wien（安特卫普大学; 代尔夫特理工大学; 维也纳科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出功能聚合查询作为统一框架，通过InsideOut评估方案统一并扩展量子电路的经典模拟，并引入张量布局对称宽度作为新的可处理性标准。
AI 中文摘要
我们将功能聚合查询（FAQs）确立为量子电路精确经典模拟的统一语言。电路成为求和-乘积查询：因子编码门，内部线变量被聚合，自由边界变量索引跃迁振幅。核心见解是，不同的模拟可处理性来源可以在同一InsideOut评估方案中加以利用。查询指定计算内容；评估计划、半环和中间因子的表示决定成本。这一观点统一了结构性和代数性模拟保证。通过显式因子表示，FAQ评估恢复了张量网络收缩的树宽界限，并通过分数覆盖产生更精细的稀疏敏感界限。在形式相位半环上，压缩中间因子恢复了兼容二次相位表示的基于秩宽的模拟。对于Clifford电路，仿射-二次因子在乘法和边缘化下封闭，并保持多项式大小，从而在无需任何有界宽度假设的情况下实现多项式时间精确振幅计算。除这些恢复外，该框架产生了一个新的可处理性标准：张量布局对称宽度。该参数通过精确树-张量表示结合局部割秩与分隔符对称性。我们给出了一个构造性评估界限，并展示了一个具有有界张量布局对称宽度但无界相位图秩宽和电路线图树宽的电路族。这些结果确立了表示感知的FAQ评估作为经典模拟的通用算法基础，以及通往新可处理体系的系统路径。
英文摘要
We establish functional aggregate queries (FAQs) as a unifying language for exact classical simulation of quantum circuits. A circuit becomes a sum-product query: factors encode gates, internal wire variables are aggregated, and free boundary variables index transition amplitudes. The central insight is that distinct sources of simulation tractability can be exploited within the same InsideOut evaluation scheme. The query specifies what is computed; the evaluation plan, semiring, and representation of intermediate factors determine the cost. This view unifies structural and algebraic simulation guarantees. With explicit factor representations, FAQ evaluation recovers the treewidth bound for tensor-network contraction and yields finer sparsity-sensitive bounds via fractional covers. Over a formal phase semiring, compressed intermediate factors recover rank-width-based simulation for compatible quadratic phase representations. For Clifford circuits, affine-quadratic factors are closed under multiplication and marginalization and remain polynomial in size, yielding polynomial-time exact amplitude computation without any bounded-width assumption. Beyond these recoveries, the framework yields a new tractability criterion: tensor layout symmetry width. This parameter combines local cut-rank with separator symmetry through exact tree-tensor representations. We give a constructive evaluation bound and exhibit a circuit family with bounded tensor layout symmetry width but unbounded phase-graph rank-width and circuit line-graph treewidth. These results establish representation-aware FAQ evaluation as a common algorithmic foundation for classical simulation and a systematic route to new tractable regimes.
Comments50 pages
