Dequantization of quantum machine learning models is the methodology of creating an equivalent classical model using a partial Fourier series over the classical input variables such that the classical model can be efficiently run on a classical computer whilst being as accurate as its quantum counterpart. In this paper, we present an experimental validation of the dequantization of quantum machine learning models using realworld WiFi localization dataset. The classical surrogate model necessitates the same amount order-of-magnitude parameters in the worst case without any statistically significant reduction in accuracy. At the same time, it demonstrates the usefulness of quantum machine learning to obtain an efficient and accurate classical model for classification and regression tasks.
Dequantization of quantum machine learning models is the methodology of creating an equivalent classical model using a partial Fourier series over the classical input variables such that the classical model can be efficiently run on a classical computer whilst being as accurate as its quantum counterpart. In this paper, we present an experimental validation of the dequantization of quantum machine learning models using realworld WiFi localization dataset. The classical surrogate model necessitates the same amount order-of-magnitude parameters in the worst case without any statistically significant reduction in accuracy. At the same time, it demonstrates the usefulness of quantum machine learning to obtain an efficient and accurate classical model for classification and regression tasks.
Abstract Surrogates have been proposed as classical simulations of the pretrained quantum learning models, which are capable of mimicking the input-output relation inherent in the quantum model. Quantum hardware within this framework is used for training and for generating the classical surrogates. Inference is relegated to the classical surrogate, hence alleviating the extra quantum computational cost once training is done. Taking inspiration from interpretable models, we introduce a local surrogation protocol based on reuploading-type quantum learning models, including local quantum surrogates as cost-efficient intermediate quantum learning models. When the training and inference are only concerned with a subregion of the data space, deploying a local quantum surrogate offers qubit cost reductions and the downstream local classical surrogate achieves dequantization of the inference phase. Several numerical experiments are presented.
In the quest for quantum advantage, a central question is under what conditions can classical algorithms achieve a performance comparable to quantum algorithms--a concept known as dequantization. Random Fourier features (RFFs) have demonstrated potential for dequantizing certain quantum neural networks (QNNs) applied to regression tasks, but their applicability to other learning problems and architectures remained unexplored. In this work, we derive bounds on the true risk gap between classical RFF models and quantum models for regression and classification tasks with both QNN and quantum kernel architectures. Furthermore, we provide sufficient conditions under which this gap is small and thus the quantum system can be dequantized via the RFF method. We support our findings with numerical experiments that illustrate the practical dequantization of existing quantum kernel-based methods. Our findings not only broaden the applicability of RFF-dequantization but also enhance the understanding of potential quantum advantages in practical machine-learning tasks.
Abstract Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.
Abstract Quantum Machine Learning algorithms based on Variational Quantum Circuits (VQCs) are important candidates for useful application of quantum computing. It is known that a VQC is a linear model in a feature space determined by its architecture. Such models can be compared to classical ones using various sets of tools, and surrogate models designed to classically approximate their results were proposed. At the same time, quantum advantages for learning tasks have been proven in the case of discrete data distributions and cryptography primitives. In this work, we propose a framework to avoid Random Feature approximation techniques. Using previous results, we establish conditions on the weight vectors of the quantum models that are necessary to avoid these dequantization methods. We show that this theory is compatible with previously proven quantum advantages on discrete inputs, and provides examples of advantages for continuous inputs. This separation is connected to large weight vector norm, and we suggest that this can only happen with a high dimensional feature map. Our results demonstrate that it is possible to design quantum models that cannot be classically approximated with good generalization. In addition, we provide a method to verify that the necessary condition is respected for a quantum model. Finally, we discuss how concentration issues must be considered to design such instances. We expect that our work will be a starting point to design near-term quantum models that avoid dequantization methods by ensuring non-classical convergence properties, and to identify existing quantum models that can be classically approximated.
There is currently a huge effort to understand the potential and limitations of variational quantum machine learning (QML) based on the optimization of parameterized quantum circuits. Recent proposals toward dequantizing variational QML models for regression problems include approaches based on kernel methods with carefully chosen kernel functions, approximated via Random Fourier Features (RFF). In this short note we show that for a wide range of instances, this approach can be simplified. More specifically, we show that the kernels whose evaluation is approximated by RFF in this dequantization algorithm can in fact often be evaluated exactly and efficiently classically. As such, our results enhance the toolkit for kernel-based dequantization of variational QML.
Quantum Machine Learning (QML) is emerging as a promising technology for tackling complex computational challenges, although its practical implementation faces significant obstacles owed to the inherent noise in current quantum devices. This paper presents a hybrid architecture that combines classical and quantum elements for the development and training of QML models under noisy conditions. This research evaluates the impact of noise on superconducting systems through emulation. The study shows that, compared to noise-free configurations, certain noise levels tend to allow for a reduction in the number of qubits, thus simplifying the architecture of the quantum neural network, which has a direct impact on the computational cost and execution times. Experimental validation was performed by applying three biomedical datasets related to breast cancer detection. The experimental findings revealed that the variations in accuracy between noiseless configurations and those subjected to noisy conditions were minimal, with deviations ranging from 0.11% to 1.68%. Additionally, it was observed that the incorporation of noise during training contributed positively to the efficiency of the process for the datasets under test, achieving improvements in training execution times ranging from a factor of 1.61 to 4.39, when the proposed architecture was emulated on Qaptiva 802.