Markovian Quantum Neuroevolution for Machine Learning

Neuroevolution, a field that draws inspiration from the evolution of brains in nature, harnesses evolutionary algorithms to construct artificial neural networks. It bears a number of intriguing capabilities that are typically inaccessible to gradient-based approaches, including optimizing neural-network architectures, hyperparameters, and even learning the training rules. In this paper, we introduce a quantum neuroevolution algorithm that autonomously finds near-optimal quantum neural networks for different machine-learning tasks. In particular, we establish a one-to-one mapping between quantum circuits and directed graphs, and reduce the problem of finding the appropriate gate sequences to a task of searching suitable paths in the corresponding graph as a Markovian process. We benchmark the effectiveness of the introduced algorithm through concrete examples including classifications of real-life images and symmetry-protected topological states. Our results showcase the vast potential of neuroevolution algorithms in quantum architecture search, which would boost the exploration towards quantum-learning advantage with noisy intermediate-scale quantum devices.

Figure 1

Schematic illustration of the MQNE algorithm. For a given quantum machine-learning (QML) problem and experimental setup, we first determine the allowed gate blocks and the corresponding directed graph, and iteratively generate quantum circuits in a Markovian fashion. The algorithm terminates when the highest fitness of the generated circuits becomes larger than a certain threshold value $f_c$ or the number of generations exceeds a given number $g_c$.

Figure 2

Numerical results for classification of handwritten-digit images in the MNIST dataset. In (a), the initial variational parameters of single-qubit rotation gates are randomly chosen during the training process. In (b), we plot the loss and accuracy as a function of training epochs for the sixth-generation quantum circuit with the highest fitness. (c) The fitness of generated circuits for each generation with fixed initial variational parameters and (d) plots the loss and accuracy for the sixth-generation circuit that has largest fitness [86].

Figure 3

Performance of the MQNE algorithm in the task of classifying symmetry-protected topological states [86].