近日，美国IBM量子公司的Kristan Temme及其研究团队取得一项新进展。经过不懈努力，他们提出群结构数据的协变量子核函数。相关研究成果已于2024年1月19日在国际知名学术期刊《自然—物理学》上发表。

该研究团队针对具有组结构的数据确定了一类适合使用核方法的学习问题。为了解决这些问题，研究人员引入了一组量子核，这些量子核可以应用于这些数据，并从已知的、在解决一组特定问题时具有量子经典分离的核进行推广。为了验证他们的方法，研究人员使用了超导处理器的27个量子比特，并选择了一个学习问题来体现群组上许多基本学习问题的结构。

据悉，核函数是用于从数据集中提取重要特征的常用技术。在量子计算领域，量子计算机可以用来估计作为幺正电路跃迁幅度的核项。然而，量子核的存在性受到计算硬度假设的限制，因此不能被经典方法计算。在这种情况下，学习问题通常是人为构建的，因此找到与现实世界数据相关的量子核成为了一个重要的挑战。

附：英文原文

Title: Covariant quantum kernels for data with group structure

Author: Glick, Jennifer R., Gujarati, Tanvi P., Crcoles, Antonio D., Kim, Youngseok, Kandala, Abhinav, Gambetta, Jay M., Temme, Kristan

Issue&Volume: 2024-01-19

Abstract: The use of kernel functions is a common technique to extract important features from datasets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to computational hardness assumptions, cannot be computed classically. The learning problems for these cases are constructed artificially and it is an important challenge to find quantum kernels that have the potential to be relevant for real-world data. Here we identify a suitable class of learning problems on data that have a group structure, which are amenable to kernel methods. We introduce a family of quantum kernels that can be applied to such data, generalizing from a kernel that is known to have a quantum–classical separation when solving a particular set of problems. We use 27 qubits of a superconducting processor to demonstrate our method with a learning problem that embodies the structure of many essential learning problems on groups.

DOI: 10.1038/s41567-023-02340-9

Source: https://www.nature.com/articles/s41567-023-02340-9