Demonstration of coherent control and characterization of the control fidelity is important for the development of quantum architectures such as nuclear magnetic resonance (NMR). We introduce an experimental approach to realize universal quantum control, and benchmarking thereof, in zero-field NMR, an analog of conventional high-field NMR that features less-constrained spin dynamics. We design a composite pulse technique for both arbitrary one-spin rotations and a two-spin controlled-not (CNOT) gate in a heteronuclear two-spin system at zero field, which experimentally demonstrates universal quantum control in such a system. Moreover, using quantum information-inspired randomized benchmarking and partial quantum process tomography, we evaluate the quality of the control, achieving single-spin control for ¹³C with an average fidelity of 0.9960(2) and two-spin control via a CNOT gate with a fidelity of 0.9877(2). Our method can also be extended to more general multispin heteronuclear systems at zero field. The realization of universal quantum control in zero-field NMR is important for quantum state/coherence preparation, pulse sequence design, and is an essential step toward applications to materials science, chemical analysis, and fundamental physics.

中文翻译：

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零场核磁共振中量子控制的实验基准测试。

证明相干控制和控制保真度的特性对于开发诸如核磁共振（NMR）的量子体系结构非常重要。我们介绍一种实验方法，以在零场NMR中实现通用量子控制并对其进行基准测试，该零场NMR是传统的高场NMR的类似物，其自旋动力学约束较小。我们设计了一种在零场的异核两轴系统中针对任意一轴旋转和两轴非控制（CNOT）门的复合脉冲技术，该实验通过实验证明了这种系统中的通用量子控制。此外，利用量子信息启发的随机基准测试和部分量子过程层析成像技术，我们评估了控制的质量，实现了^13种单旋控制C的平均保真度为0.9960（2），并通过CNOT门进行两转控制，保真度为0.9877（2）。我们的方法还可以扩展到零场下更通用的多旋异核系统。零场NMR中通用量子控制的实现对于量子态/相干制备，脉冲序列设计非常重要，并且是向材料科学，化学分析和基础物理学应用的必不可少的步骤。