Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many important theoretical properties of these models remain unknown. Here we investigate how the strategy with which data is encoded into the model influences the expressive power of parametrised quantum circuits as function approximators. We show that one can naturally write a quantum model as a partial Fourier series in the data, where the accessible frequencies are determined by the nature of the data encoding gates in the circuit. By repeating simple data encoding gates multiple times, quantum models can access increasingly rich frequency spectra. We show that there exist quantum models which can realise all possible sets of Fourier coefficients, and therefore, if the accessible frequency spectrum is asymptotically rich enough, such models are universal function approximators.
Maximising Quantum-Computing Expressive Power through Randomised Circuits
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
Enhancing the reachability of variational quantum algorithms via input-state design
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿科学学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（教育部量子物理与光子量子信息重点实验室，电子科技大学）；Shimmer Center, Tianfu Jiangxi Laboratory（天府江西实验室 shimmer 中心）
Matrix encoding method in variational algorithm of calculating eigenvalues and generalized eigenvalues
Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS（俄罗斯科学院化学物理与医药化学问题联邦研究中心）；School of Mathematical Sciences, Zhejiang University（浙江大学数学科学学院）
Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits
Georgia Institute of Technology（佐治亚理工学院）；NVIDIA Research（NVIDIA研究）；IBM Research（IBM研究）；Hon Hai (Foxconn) Quantum Computing Research Center（鸿海（富士康）量子计算研究中心）
Qubit-Efficient Variational Quantum Optimization via Pauli Correlation Encoding: Application to Large-Scale Power Demand Portfolio Optimization
Strategic Technology Center, TISI Inc.（TISI公司战略技术中心）；Graduate School of Engineering Science, Osaka University（大阪大学工程科学研究科）；Center for Quantum Information and Quantum Biology, Osaka University（大阪大学量子信息与量子生物学中心）；Center for Quantum Computing, RIKEN（理化学研究所量子计算中心）
A Resource-Efficient Variational Quantum Framework for the Traveling Salesman Problem
Shenzhen SpinQ Technology Co., Ltd（深圳启元科技有限公司）；School of Energy Storage Science and Engineering, North China University of Technology（华北电力大学能源存储科学与工程学院）
Supervised Learning Using a Dressed Quantum Network with "Super Compressed Encoding": Algorithm and Quantum-Hardware-Based Implementation
Indian Institute of Technology Delhi（印度理工学院德里分校）
已知在有噪声的中间尺度量子（NISQ）设备上实现变分量子机器学习（QML）算法具有与所需的大量量子比特和与多量子比特门相关联的噪声有关的问题。在本文中，我们提出了一个变分QML算法，使用一个穿着量子网络来解决这些问题。使用我们在这里遵循的“超压缩编码”方案，在将输入馈送到变分量子线路之前，我们的修饰网络中的经典编码层大幅降低了输入维度。因此，我们的量子线路所需的量子比特数量急剧下降。此外，与大多数其他现有的QML算法不同，我们的量子线路仅由单量子比特门组成，使其对噪声具有鲁棒性。这些因素使我们的算法适合NISQ硬件上实现。为了支持我们的论点，我们在真实的NISQ硬件上实现了我们的算法，从而使用流行的机器学习数据集（如Fisher's Iris，Wisconsin's Breast Cancer（WBC）和Abalone）显示了准确的分类。然后，为了给我们的算法的工作提供一个直观的解释，我们展示了量子态的聚类，它对应于不同的输出类的输入样本，在Bloch球（使用WBC和MNIST数据集）。这种聚类是我们算法中训练过程的结果。通过这种基于布洛赫球的表示，我们还显示了经典编码层的可调参数和变分量子线路的可调参数（在训练中）所起的不同作用。这些参数在训练期间通过损失最小化迭代地调整。
