散粒噪声对NMR谱量子计算的影响

中文摘要 AI 辅助

量子计算硬件领域的最新进展推动了寻找展示所谓量子优势的应用。一个已被识别出的有前景用例是多体量子系统的模拟。在经典计算机上执行此类模拟所需的计算资源通常随被建模系统的规模呈指数增长，这最终归因于系统动力学所发生的希尔伯特空间的指数增长。虽然数字量子计算机原生地在这样的希尔伯特空间中直接演化量子态，从而在表面上避免了这一问题，但此类计算的结果通常并非以确定性输出获得。相反，它需要投影测量，而这些测量从根本上受到散粒噪声的影响。任何期望的期望值因此必须通过重复测量来重建，使得这些测量的次数成为一种相关的计算资源，从而成为任何潜在量子优势声明的重要考量。在本工作中，我们以核磁共振（NMR）谱的模拟作为测试案例，研究了该资源如何随系统规模变化（这种变化本身取决于最终结果的期望精度）。我们针对真实世界分子以及一类模型NMR哈密顿量研究了这种变化，后者允许对一维、二维和全连接相互作用进行高效的大规模模拟。我们发现所需资源仅随分子尺寸弱增长，远低于底层希尔伯特空间的指数增长。这一结果表明，散粒噪声不应构成在NMR系统模拟中实现量子优势的根本障碍，或许对于更广泛的多体系统也是如此。

英文摘要

Recent advances in the field of quantum computing hardware motivate the search for applications which demonstrate so-called quantum advantage. One promising use case that has been identified is the simulation of quantum many-body systems. The computational resources required for performing such a simulation on a classical computer generally grow exponentially with the size of the system being modeled, which is ultimately due to the exponential growth of the Hilbert space in which the dynamics of such a system take place. While digital quantum computers natively evolve quantum states directly in such a Hilbert space, thus naively avoiding this problem, the result of such a computation is typically not obtained as a deterministic output. Rather, it requires projective measurements which are fundamentally affected by shot noise. Any desired expectation values must therefore be reconstructed from repeated measurements, making the number of those measurements a relevant computational resource, and thus an important consideration for any potential claims of quantum advantage. In this work, we study how this resource scales with system size (a scaling which itself depends on the desired accuracy of the final result), using the simulation of nuclear magnetic resonance (NMR) spectra as a test case. We study this scaling for both real-world molecules, as well as a class of model NMR Hamiltonians which allow for efficient large-scale simulations with one-dimensional, two-dimensional, and all-to-all interactions. We find that the required resources increase only weakly with molecular size, far below the exponential growth of the underlying Hilbert space. This result suggests that shot noise should not pose a fundamental barrier to achieving quantum advantage in the simulation of NMR systems, and perhaps for many-body systems more broadly.

发表机构

• Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学理论物理研究所与集成量子科学与技术中心）
• HQS Quantum Simulations GmbH（HQS量子模拟有限公司）
• The University of Nottingham（诺丁汉大学）

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