VQC can be understood through the lens of Fourier analysis. It is already well-known that the function space represented by any circuit architecture can be described through a truncated Fourier sum. We show that the spectrum available to that truncated Fourier sum is not entirely determined by the encoding gates of the circuit, since the variational part of the circuit can constrain certain coefficients to zero, effectively removing that frequency from the spectrum. To the best of our knowledge, we give the first description of the functional dependence of the Fourier coefficients on the variational parameters as trigonometric polynomials. This allows us to provide an algorithm which computes the exact spectrum of any given circuit and the corresponding Fourier coefficients. Finally, we demonstrate that by comparing the Fourier transform of the dataset to the available spectra, it is possible to predict which VQC out of a given list of choices will be able to best fit the data.
Sub-universal variational circuits for combinatorial optimization problems
Department of Physics, University of Colorado Boulder, Boulder, CO 80309, USA（科罗拉多大学博尔德分校物理系）；University of Technology Sydney, Centre for Quantum Software（悉尼技术大学量子软件中心）；Department of Electrical, Computer and Energy Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA（科罗拉多大学博尔德分校电气、计算机与能源工程系）
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）
Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems
Institute for Advanced Study（高等研究院）；Samsung Research（三星研究院）；Korea Institute for Advanced Study（韩国高等研究院）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
Image Classification with Rotation-Invariant Variational Quantum Circuits
Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA)（伊克兰技术研究中心、巴斯克研究与技术联盟）；Donostia International Physics Center（多诺西亚国际物理中心）
Orthogonally Decoupled Variational Fourier Features
Dalle Molle Institute for Artificial Intelligence (IDSIA)（Dalle Molle人工智能研究所 (IDSIA)）；Università della Svizzera Italiana (USI)（瑞士意大利语区大学 (USI)）；University of Limerick (UL)（利默里克大学 (UL)）
Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits
University of California, Berkeley（加州大学伯克利分校）；Stanford University（斯坦福大学）；St. Kliment Ohridski University of Sofia（索非亚圣克里门特·奥赫里德大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks
School of Integrated Technology, Yonsei University, Incheon 21983, Republic of Korea（延世大学集成技术学院）；Department of Quantum Information, Yonsei University, Incheon 21983, Republic of Korea（延世大学量子信息系）
