Developments of quantum techniques have drastically improved the control ability of current quantum processors. Characterizing quantum simulations performed on these processors has become a vital topic in quantum information processing. Traditional characterizing techniques such as quantum process and state tomography fully characterize quantum simulations, but always with the exponentially increased resource cost, unfortunately. It may place their applications only in small-scale quantum systems. Meanwhile, many potential characterizing methods have been put forward in the past decades. In this work we experimentally test and compare different methods for characterizing quantum simulations of Ising Hamiltonians on the nuclear magnetic resonance (NMR) platform, including the recent quantum Hamiltonian tomography with polynomial complexity to estimate the generator of quantum simulations and nonrepetitive direct fidelity estimation with the Monte Carlo method to estimate the fidelity of dynamical states. We also experimentally estimate the parameters of Hamiltonian via full quantum process tomography and quantum state tomography for the comparison. These methods have merits and demerits in accuracy, the required resource, and prior knowledge. Our experiments test the performance of different methods while providing a beneficial reference for characterizing quantum simulations in the future.

中文翻译：

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在自旋量子模拟器上用量子层析成像表征量子模拟

量子技术的发展极大地提高了当前量子处理器的控制能力。表征在这些处理器上执行的量子仿真已成为量子信息处理中的重要课题。传统的表征技术（例如量子过程和状态层析成像）完全可以表征量子模拟，但是不幸的是，资源成本始终呈指数增长。它可能仅将其应用放在小规模的量子系统中。同时，在过去的几十年中已经提出了许多潜在的表征方法。在这项工作中，我们通过实验测试和比较了在核磁共振（NMR）平台上表征Ising哈密顿量的量子模拟的不同方法，包括最近的具有多项式复杂度的量子哈密顿量层析成像以估计量子模拟的生成器，以及使用蒙特卡洛方法的非重复直接保真度估计以估计动态状态的保真度。我们还通过全量子过程层析成像和量子态层析成像实验性地估计了哈密顿量的参数，以进行比较。这些方法在准确性，所需资源和先验知识方面各有优缺点。我们的实验测试了不同方法的性能，同时为将来表征量子模拟提供了有益的参考。我们还通过全量子过程层析成像和量子态层析成像实验性地估计了哈密顿量的参数，以进行比较。这些方法在准确性，所需资源和先验知识方面各有优缺点。我们的实验测试了不同方法的性能，同时为将来表征量子模拟提供了有益的参考。我们还通过全量子过程层析成像和量子态层析成像实验性地估计了哈密顿量的参数，以进行比较。这些方法在准确性，所需资源和先验知识方面各有优缺点。我们的实验测试了不同方法的性能，同时为将来表征量子模拟提供了有益的参考。