Atomic-level qubits in silicon are attractive candidates for large-scale quantum computing; however, their quantum properties and controllability are sensitive to details such as the number of donor atoms comprising a qubit and their precise location. This work combines machine learning techniques with million-atom simulations of scanning tunnelling microscopic (STM) images of dopants to formulate a theoretical framework capable of determining the number of dopants at a particular qubit location and their positions with exact lattice site precision. A convolutional neural network (CNN) was trained on 100,000 simulated STM images, acquiring a characterisation fidelity (number and absolute donor positions) of >98% over a set of 17,600 test images including planar and blurring noise commensurate with experimental measurements. The formalism is based on a systematic symmetry analysis and feature-detection processing of the STM images to optimise the computational efficiency. The technique is demonstrated for qubits formed by single and pairs of closely spaced donor atoms, with the potential to generalise it for larger donor clusters. The method established here will enable a high-precision post-fabrication characterisation of dopant qubits in silicon, with high-throughput potentially alleviating the requirements on the level of resources required for quantum-based characterisation, which will otherwise be a challenge in the context of large qubit arrays for universal quantum computing.

硅中的原子级量子位是大规模量子计算的诱人候选。然而，它们的量子性质和可控性对细节敏感，例如组成一个量子位的供体原子的数量及其精确位置。这项工作将机器学习技术与掺杂物的扫描隧道显微镜（STM）图像的百万个原子模拟相结合，从而形成了一种理论框架，该框架能够确定特定量子位位置处的掺杂物数量及其位置，并具有精确的晶格位置精度。在100,000张模拟STM图像上训练了卷积神经网络（CNN），在包括平面和模糊噪声的17,600张测试图像中获得了大于98％的表征保真度（数量和绝对供体位置），包括与实验测量值相对应的噪声。形式主义基于对STM图像的系统对称性分析和特征检测处理，以优化计算效率。演示了该技术用于由一对和一对紧密间隔的施主原子形成的量子位，并有可能将其推广到较大的施主簇。此处建立的方法将能够对硅中的掺杂物量子位进行高精度的后加工表征，而高通量可能会减轻基于量子表征所需的资源水平要求，否则这将成为挑战。用于通用量子计算的大型量子位阵列。演示了该技术用于由一对和一对紧密间隔的施主原子形成的量子位，并有可能将其推广到较大的施主簇。此处建立的方法将能够对硅中的掺杂物量子位进行高精度的后加工表征，而高通量可能会减轻基于量子表征所需的资源水平要求，否则这将成为挑战。用于通用量子计算的大型量子位阵列。演示了该技术用于由一对和一对紧密间隔的施主原子形成的量子位，并有可能将其推广到较大的施主簇。此处建立的方法将能够对硅中的掺杂物量子位进行高精度的后加工表征，而高通量可能会减轻基于量子表征所需的资源水平要求，否则这将成为挑战。用于通用量子计算的大型量子位阵列。