发表机构
Quantum Software Lab; University of Edinburgh, UK; IBM Research; Centre for Quantum Technologies; National University of Singapore（量子软件实验室; 爱丁堡大学; IBM研究院; 量子技术中心; 新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究表明纠缠几何约束电路切割等属性，具恒定接缝键维度的MPS和TTN电路可经典模拟，构建的双块电路家族可廉价切割，MPS硬度和可训练性深度范围不兼容，用魔法作硬度资源可避免冲突，浅Clifford+\(T\)电路有相应特性。
AI 中文摘要
电路切割有望扩展量子计算规模，但变分量子优势还需低切割开销、经典硬度和可训练性。我们表明这些属性受纠缠几何强烈约束。具有恒定接缝键维度的矩阵乘积态（MPS）和树张量网络（TTN）电路可在\(O(1/\varepsilon^2)\)采样开销下切割，但仍可高效经典模拟，排除了这些家族内的渐近量子优势。通过独立控制接缝和块内纠缠，我们构建了一个双块电路家族，它可廉价切割且需要超多项式全局MPS键维度，数值上支持到\(n = 100\)。然而，MPS硬度和可训练性需要不兼容的深度范围，分别为\(d=\omega(\log n)\)和\(d=O(\log n)\)。使用魔法而非纠缠作为硬度资源可避免此冲突：浅的Clifford+\(T\)电路可切割且可训练，同时其稳定器模拟成本随\(T\)计数呈指数增长。
英文摘要
Circuit cutting promises to scale quantum computations beyond current hardware, but variational quantum advantage also requires low cutting overhead, classical hardness, and trainability. We show that these properties are strongly constrained by entanglement geometry. Matrix product state (MPS) and tree tensor network (TTN) circuits with constant seam bond dimension can be cut with \(O(1/\varepsilon^2)\) sampling overhead, but remain efficiently classically simulable, ruling out asymptotic quantum advantage within these families. By independently controlling seam and intra-block entanglement, we construct a two-block circuit family that remains cheaply cuttable while requiring a super-polynomial global MPS bond dimension, as supported numerically up to \(n=100\). However, MPS hardness and trainability require incompatible depth regimes, \(d=ω(\log n)\) and \(d=O(\log n)\), respectively. Using magic rather than entanglement as the hardness resource avoids this conflict: shallow Clifford+\(T\) circuits remain cuttable and trainable while their stabiliser-simulation cost grows exponentially with the \(T\)-count.
Comments4 pages, 2 figures
