AI 中文总结
研究团队在Quantinuum H2-2囚禁离子处理器上开发保结构傅里叶量子电路，模拟一维、二维声学波动方程及变质量狄拉克动力学，以子区域动能为观测指标，获平均绝对误差5.9×10⁻³至2.4×10⁻²的结果，证明可解析结构化波动问题的可观测量动力学。
AI 中文摘要
波动方程为近期偏微分方程的量子模拟提供了天然测试平台，但硬件演示在空间维度、方程类型、系统规模及具有物理意义的输出方面仍存在局限。我们在Quantinuum H2-2囚禁离子处理器上开发并基准测试了基于傅里叶变换的保结构量子电路，用于一维、二维声学波动方程及变质量狄拉克动力学。实验包含最多1024个点的一维网格、32×32的二维网格，对应编码态空间维度最高达4096。我们未重构完整场，而是直接从测量样本估计子区域动能。在所有测试的声学与狄拉克动力学问题中，H2-2的结果与经典动能动力学的平均绝对误差介于5.9×10⁻³至2.4×10⁻²之间；在固定保留带宽下，编译后的门数量随网格量子比特数近似二次增长，声学电路规模基本与演化时间无关，而狄拉克动力学的成本还随乘积公式步数增加。这些结果提供了硬件层面的证据，表明在当前囚禁离子处理器上，针对具有数千个编码自由度的结构化波动问题，可解析出准确的可观测量动力学。
英文摘要
Wave equations provide a natural testbed for near-term quantum simulation of partial differential equations, but hardware demonstrations have remained limited in spatial dimension, equation class, system size, and physically meaningful output. We develop and benchmark structure-preserving, Fourier-based quantum circuits for the one- and two dimensional acoustic wave equations and Dirac dynamics with variable mass on the Quantinuum H2-2 trapped-ion processor. The experiments include one-dimensional grids with up to \(1024\) points and \(32\times32\) two-dimensional grids, corresponding to an encoded state-space dimension of up to \(4096\). Rather than reconstructing the full fields, we estimate subdomain kinetic energies directly from measurement samples. Across all tested acoustic and Dirac dynamics problems, the H2-2 results track the classical kinetic-energy dynamics with mean absolute errors between \(5.9\times10^{-3}\) and \(2.4\times10^{-2}\). At fixed retained bandwidth, the compiled gate counts grow approximately quadratically with the number of grid qubits; the acoustic circuit sizes are essentially independent of evolution time, whereas the cost also grows with the number of product-formula steps. These results provide hardware-level evidence that accurate observable dynamics can remain resolvable for structured wave problems with thousands of encoded degrees of freedom on a present-day trapped-ion processor.
