Quantum Machine Learning (QML) is one of promising applications for near-term quantum computing. Two popular methods in QML are kernel methods and variational methods. Variational methods, which consist of parametrized quantum circuits (PQCs) to encode data and define classifiers, work faster in theory (i.e., O(N) to learn from
Ntraining examples) than kernel methods, which use quantum circuits to compute O(N2) elements of kernel matrices. However, in practice when dealing with large N, it is necessary to speed up variational methods due to the slow quantum gates. In this work, we propose a parallelization of training variational quantum classifiers to utilize the availability of many quantum devices with dozens of qubits. In contrast to existing parallelization of variational methods with gradient-based algorithms, we develop a novel distributed coordinate descent algorithm to optimize parametrized gates of variational quantum circuits. There are several gradient-free methods to optimize PQCs that have been shown to converge faster. Here, by focusing on the so-called Free-axis selection (Fraxis) method, we show how the gradient-free methods can be parallelized, and demonstrate their efficacies by running the algorithm on both simulators and IBM Quantum devices. We confirm the proposed algorithm achieves high classification accuracy and gains almost-linear speedup with the degree of parallelization.
A quantum variational circuit is a quantum machine learning model similar to a neural network. A crafted adversarial example can lead to incorrect results for the model. Using adversarial examples to train the model will greatly improve its robustness. The existing method is to use automatic differentials or finite difference to obtain a gradient and use it to construct adversarial examples. This paper proposes an innovative method for constructing adversarial examples of quantum variational circuits. In this method, the gradient can be obtained by measuring the expected value of a quantum bit respectively in a series quantum circuit. This method can be used to construct the adversarial examples for a quantum variational circuit classifier. The implementation results prove the effectiveness of the proposed method. Compared with the existing method, our method requires fewer resources and is more efficient.
We have developed two quantum classifier models for the ttH classification problem, both of which fall into the category of hybrid quantumclassical algorithms for Noisy Intermediate Scale Quantum devices (NISQ). Our results, along with other studies, serve as a proof of concept that Quantum Machine Learning (QML) methods can have similar or better performance, in specific cases of low number of training samples, with respect to conventional ML methods even with a limited number of qubits available in current hardware. To utilise algorithms with a low number of qubits — to accommodate for limitations in both simulation hardware and real quantum hardware — we investigated different feature reduction methods. Their impact on the performance of both the classical and quantum models was assessed. We addressed different implementations of two QML models, representative of the two main approaches to supervised quantum machine learning today: a Quantum Support Vector Machine (QSVM), a kernel-based method, and a Variational Quantum Circuit (VQC), a variational approach.