arXiv 2510.009352025-10quant-ph

张量网络与QUBO嵌入的块编码

Tensor Networks as an Explicit Interface for Quantum Block-Encodings

Sebastian Issel

AI总结：

该研究提出了一种将张量网络转换为块编码单元ary序列的算法，并展示了如何将QUBO问题映射到MPO和通用张量网络的方法。

摘要：

我们提供了一个算法，将任何张量网络（TN）转换为一系列局部单元ary，其组合块编码网络收缩，适用于量子特征值/奇异值变换（QET/QSVT）。该构造将每个TN嵌入为局部等距映射，并将其扩展为单位ary。对每个张量的每个站点执行此步骤，使整个网络得以块编码。该理论不依赖于虚拟键大小；对于量子比特资源计数和示例，我们假设全局2的幂次填充。此外，我们还提出了一种确定性的扫掠方法，将二次无约束二元优化（QUBO）/异斯金哈密顿量映射到矩阵积算符（MPO）和通用张量网络。我们提供了正式陈述、伪代码、资源公式以及该方法在状态准备和学习一般量子算符中的应用讨论。

英文摘要：

Tensor networks (TNs) give explicit classical descriptions of structured finite linear maps, while block-encodings (BEs) are the standard quantum access model for such maps. We establish TNs as a universal data interface for quantum algorithms: any explicitly specified TN for an arbitrary finite linear map compiles directly to an explicit qubit BE, with no penalty on the selected-block round trip under faithful compression. Along a chosen sweep, the compiler handles local non-unitarity by exact local dilations and aggregates the resulting post-selection conditions online using logarithmically many additional flag qubits. The chosen sweep incurs three exact, sweep-dependent costs (the accumulated scale, the frontier memory, and the number of genuinely dilated local steps), which the main theorems are stated in terms of. In the bounded-local explicit arithmetic model, this yields linear-time compilation to linear-size circuits with constant-size local gadgets, and hence a constant-factor size correspondence between bounded-local TNs and bounded-local BEs. The same construction gives a selected-block round trip BE->TN->BE: a BE canonically yields a TN for its selected block rather than for an arbitrary unitary extension, which can then be compressed or approximated classically before recompilation. Faithful Schmidt-rank compression transfers monotonically (the scale cost and frontier memory cannot increase, with operator error bounded by the discarded weight), while arbitrary restructuring admits no general scale guarantee, a limitation we show is unavoidable. As consequences and limits of this scale accounting, we characterize exact scale optimality, show that bridge-hourglass forests admit scale-optimal sweeps after exact recursive local bond compression, and prove that certifying unrestricted exact scale optimality is already hard for diagonal MPOs on a path unless P=NP.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文