发表机构
Phasecraft; Virginia Tech; Harvard University; University College London（Phasecraft; 弗吉尼亚理工大学; 哈佛大学; 伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对被全局酉变换隐藏的非相互作用哈密顿量，提出SPICES方法，结合Hadamard测试与经典后处理，高效恢复谱分布，并证明问题为DQC1难。该方法有望推动材料模拟的量子应用。
AI 中文摘要
我们在一种新颖的设置中研究哈密顿量学习，其中我们被承诺存在一种被全局酉变换所混淆的物理结构。具体而言，我们考虑学习哈密顿量 $H=U^{\dagger}(\sum_{i \in I} E_i n_i + H_O)U$ 的权重 $E_i$ 的任务，该哈密顿量由一组非相互作用模式 $I$ 和作用于不相交模式集 $O$ 上的任意“旁观者” $H_O$ 组成。非相互作用结构被一个未知的全局酉变换 $U$ 隐藏，我们的目标是在不重构 $U$ 的情况下恢复 $E_i$。这类哈密顿量在材料建模场景中具有充分动机，它们可应用于平均场理论、格林函数和密度泛函理论等经典方法。我们证明，尽管非相互作用结构看似简化了问题，该问题仍是 DQC1-难的。随后我们引入 SPICES（通过轮廓估计器进行单粒子推断），它将 Hadamard 测试与一种新颖的经典后处理过程相结合，在特定自然假设下高效地恢复 Wasserstein 距离下的谱分布。该方法利用了单个准粒子的单粒子能量与复数逆温度下配分函数零点所控制的傅里叶频率之间的对应关系。由于准粒子谱在后续材料计算中普遍存在，且 SPICES 简单易行，我们期望 SPICES 是材料模拟中量子应用的一条有前景的途径。
英文摘要
We study Hamiltonian learning in a novel setting, where we are promised a physical structure that is obfuscated by a global unitary. In particular, we consider the task of learning the weights $E_i$ of a Hamiltonian $H=U^{\dagger}(\sum_{i \in I} E_i n_i + H_O)U$ comprised of a set of non-interacting modes $I$ and an arbitrary ``spectator'' $H_O$ acting on a disjoint set of modes $O$. The non-interacting structure is hidden by an unknown global unitary $U$, and our goal is to recover the $E_i$ without reconstructing $U$. Such Hamiltonians are well-motivated in the setting of materials modeling, where they find application for classical methods such as mean-field theory, Green's functions, and density functional theory. We show that this problem is DQC1-hard, despite the apparent simplification given by the non-interacting structure. We then introduce SPICES (single-particle inference via contour estimators), which combines a Hadamard test with a novel classical postprocessing procedure to efficiently recover the spectral distribution in Wasserstein distance under certain natural assumptions. The method exploits the correspondence between single-particle energies of the individual quasiparticles and the Fourier frequencies governing zeros of the partition function at complex inverse temperature. As quasiparticle spectra feature ubiquitously in downstream materials calculations, and with SPICES being simple and practical to execute, we expect that SPICES is a promising route to quantum applications in materials simulation.
Comments70 pages, 3 figures
