AI 中文总结
该研究提出基于扇出并行化的编译器，将海森堡哈密顿量模拟电路深度压缩，经资源对比与谱模拟验证，在受深度限制的量子硬件上可显著缩减深度与体积。
AI 中文摘要
含噪声中等规模量子计算机受限于电路深度，而自旋系统的乘积公式模拟会产生窄而深的电路。本文提出一种基于扇出的小工具编译器，在海森堡型核磁共振（NMR）哈密顿量的模拟中，以电路宽度换取深度。每个逻辑自旋被编码为与其相互作用度大小匹配的重复码寄存器，因此给定泡利类型的所有成对相互作用可在对数深度的CNOT扇出后并行执行，冗余寄存器为后选择提供误差检测，且不产生额外算法开销。核心结果是两种编译方案的固定协议资源对比，已编译为重六边形超导和全连接离子阱目标，覆盖一组NMR自旋系统。对于具有高度枢纽的相互作用图，体积最优调度将双量子比特深度减半，13自旋演示的体积缩小1.7倍，在重六边形架构上还减少了双量子比特门数，在研究的最高度分子的全连接架构上深度缩减达2.5倍。在全连接架构上，所有系统的双量子比特门数均增加，因此体积缩减对受深度限制的硬件是有益的。该增益随相互作用图的度不均匀性增大而提升，对于稠密均匀图则消失，此时最优方案为串行电路。我们模拟了13自旋星型系统四甲基硅烷的零场NMR谱。在从已发表的当代处理器校准缩放的噪声模型下，较浅的小工具电路仅在对其内置误差检测进行后选择后，才匹配或超越串行编译，此时错误率已降低1至1.5个数量级。我们将所得谱与独立经典计算结果进行了验证。
英文摘要
Noisy intermediate-scale quantum computers are constrained by circuit depth, while product-formula simulation of spin systems leads to narrow and deep circuits. Here we introduce a fan-out-based gadget compiler that trades circuit depth for width in simulations of Heisenberg-type nuclear magnetic resonance (NMR) Hamiltonians. Each logical spin is encoded into a small repetition-code register sized by its interaction degree, so that all pairwise interactions of a given Pauli type execute in parallel after a logarithmic-depth CNOT fan-out, and the redundant registers provide error detection for post-selection at no additional algorithmic overhead. The central result is a fixed-protocol resource comparison of the two compilations, transpiled to heavy-hex superconducting and all-to-all trapped-ion targets across a set of NMR spin systems. For interaction graphs with a high-degree hub the volume-optimal schedule halves the two-qubit depth and reduces the volume 1.7-fold for the 13-spin demonstration, which on heavy-hex also lowers the two-qubit gate count, and the depth reduction rises to 2.5-fold on all-to-all for the highest-degree molecule studied. On all-to-all the two-qubit gate count rises for every system, so the volume reduction is a benefit on depth-limited hardware. The gain grows with the degree inhomogeneity of the interaction graph and vanishes for dense uniform graphs, where the optimum is the sequential circuit. We simulate the zero-field NMR spectrum of tetramethylsilane, a 13-spin star system. Under a noise model scaled from a published present-day processor calibration, the shallower gadget circuits match or surpass the sequential compilation only after post-selection on their built-in error detection, once error rates improve by one to one and a half orders of magnitude. We verify the spectra against an independent classical computation.
