In a previous publication we proposed discrete global optimization as a method to train a strong binary classifier constructed as a thresholded sum over weak classifiers. Our motivation was to cast the training of a classifier into a format amenable to solution by the quantum adiabatic algorithm. Applying adiabatic quantum computing (AQC) promises to yield solutions that are superior to those which can be achieved with classical heuristic solvers. Interestingly we found that by using heuristic solvers to obtain approximate solutions we could already gain an advantage over the standard method AdaBoost. In this communication we generalize the baseline method to large scale classifier training. By large scale we mean that either the cardinality of the dictionary of candidate weak classifiers or the number of weak learners used in the strong classifier exceed the number of variables that can be handled effectively in a single global optimization. For such situations we propose an iterative and piecewise approach in which a subset of weak classifiers is selected in each iteration via global optimization. The strong classifier is then constructed by concatenating the subsets of weak classifiers. We show in numerical studies that the generalized method again successfully competes with AdaBoost. We also provide theoretical arguments as to why the proposed optimization method, which does not only minimize the empirical loss but also adds L0-norm regularization, is superior to versions of boosting that only minimize the empirical loss. By conducting a Quantum Monte Carlo simulation we gather evidence that the quantum adiabatic algorithm is able to handle a generic training problem efficiently.
Training Neural Networks with Universal Adiabatic Quantum Computing
Institute for Particle Physics Phenomenology, Durham University（杜伦大学粒子物理唯象学研究所）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理系）；Departamento de Física Teórica y del Cosmos, Universidad de Granada（格拉纳达大学理论物理与宇宙学系）
On the Generalization of Adversarially Trained Quantum Classifiers
Department of Computer Science, University of Birmingham, UK（英国伯明翰大学计算机科学系）；KCLIP Lab Centre for Intelligent Information Processing Systems (CIIPS) Department of Engineering, King’s College London, UK（伦敦国王学院工程系智能信息处理系统中心）
Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise
Computer Science, University of California Los Angeles（计算机科学，加州大学洛杉矶分校）；Electrical and Computer Engineering, University of California Los Angeles（电气与计算机工程，加州大学洛杉矶分校）
California Institute of Technology（加州理工学院）；DeepMind Technologies（深度思维科技公司）；Lockheed Martin Advanced Technology Center（洛克希德·马丁先进技术中心）；University of Southern California（南加州大学）
