We evaluate the particular performance of different quantum machine learning networks on a graph classification task. Quantum circuits with varying internal symmetry that completely, partially and not at all confer to the symmetry of the graph show different performance on the data set. The convergence results are inspected using a number of special graphs with particular structure. These are unlikely to occur in the training data and cover specific cases that refute the assumption that the quantum neural network learns simpler surrogate models based on the number of edges in the graph.
We evaluate the particular performance of different quantum machine learning networks on a graph classification task. Quantum circuits with varying internal symmetry that completely, partially and not at all confer to the symmetry of the graph show different performance on the data set. The convergence results are inspected using a number of special graphs with particular structure. These are unlikely to occur in the training data and cover specific cases that refute the assumption that the quantum neural network learns simpler surrogate models based on the number of edges in the graph.
Quantum computing is expected to fundamentally change computer systems in the future. Recently, a new research topic of quantum computing is the hybrid quantum–classical approach for machine learning, in which a parameterized quantum circuit, also called quantum neural network (QNN), is optimized by a classical computer. This hybrid approach can have the benefits of both quantum computing and classical machine learning methods. In this early stage, it is of crucial importance to understand the new characteristics of quantum neural networks for different machine learning tasks. In this paper, we will study quantum neural networks for the task of classifying images, which are high-dimensional spatial data. In contrast to previous evaluations of low-dimensional or scalar data, we will investigate the impacts of practical encoding types, circuit depth, bias term, and readout on classification performance on the popular MNIST image dataset. Various interesting findings on learning behaviors of different QNNs are obtained through experimental results. To the best of our knowledge, this is the first work that considers various QNN aspects for image data.
Abstract Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group Sn), and show how to build Sn-equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML.
Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data, but training and inference on large graphs are often bottlenecked by memory constraints and sparse linear-algebra workloads. Quantum computing offers an alternative set of primitives that may improve scalability for graph learning. Building on the quantum graph neural network (QGNN) framework of Liao \textit{et al.}, this work implements two representative architectures --- the Simplified Graph Convolution (SGC) and Linear Graph Convolution (LGC) models --- and evaluates them on open benchmark graph datasets and semi-supervised learning tasks using quantum simulation. We compare predictive performance and optimization behavior against classical baselines, showing that the quantum models achieve competitive performance with fewer parameters. Finally, we present a cost gradient analysis that identifies the tasks for which the models showcased are trainable. This is followed by a classical simulability study to find regimes in which the proposed circuits remain robust during training.
Abstract In this study, we compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the employed quantum circuits compatible with near-term quantum devices and use two distinct methodologies: applying randomized NNs on dimensionality-reduced data, and applying CNNs to full image data. We evaluate these approaches on three fully-classical data sets of increasing complexity: an artificial hypercube data set, MNIST handwritten digits and industrial images of practical relevance. Our study’s central goal is to shed more light on how quantum and classical models perform for various binary classification tasks and on what defines a good quantum model. To this end, our study involves a correlation analysis between classification accuracy and quantum model hyperparameters, and an analysis on the role of entanglement in quantum models, as well as on the impact of initial training parameters. We find classical and quantum-classical hybrid models achieve statistically-equivalent classification accuracies across most data sets with no approach consistently outperforming the other. Interestingly, we observe that quantum NNs show lower variance with respect to initial training parameters and that the role of entanglement is nuanced. While incorporating entangling gates seems to be generally advantageous, we also observe that their (optimizable) entangling power is not correlated with model performance. We also observe an inverse proportionality between the number of entangling gates and the average gate entangling power. Our study provides an industry perspective on quantum machine learning for practical binary image classification tasks, highlighting both current limitations and potential avenues for further research in quantum circuit design, entanglement utilization, and model transferability across varied applications.
This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2×Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.
Abstract For classification problems, ansatz circuits are an efficient and promising quantum-classical machine learning technique. However, a difficult design challenge arises: which quantum circuit should be used for model training? Low depth ansatz circuits have been used in a variety of applications in recent years. The earlier works defined several quantum circuit descriptors to evaluate an ansatz design such as the circuit expressibility, the efficiency with which a quantum circuit may exploit the Hilbert Space, and the entanglement capability, a circuit's capability of detecting data correlation. Additionally in this work, we investigate, measure, and analyze the effect of the number of ansatz repetition layers L, and the expressibility power of the data encoding module. The proposed quantum neural network classifiers were trained on four different classical datasets using 19 hardware-efficient parametrized circuits. The heuristic experimental results show that ansatz designs with high to moderate expressibiliy values outperformed ones with low expressibility values. By analyzing the circuit cost, we see a tendency toward maximizing the number of parameters which helps in the QNN model's convergence. On simulated hardware, we observe that the proposed quantum neural network achieves up to 97.5\% prediction accuracy using the angle data encoding module.