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International Conference on Information Fusion (FUSION)

Quantum Kernel Based Data Fusion

Leonhard Kunczik, Sabine Tornow

Published Jul 4, 2022• 0 citations
Publisher

Abstract

For quantum classification methods, the quantum kernel has a role in encoding the data set from its original low-dimensional real space into a high-dimensional quantum state space utilizing quantum circuits. Finding quantum kernels that provide an advantage in real-world data classification is a major challenge, especially when dealing with heterogeneous data or a large data set, requiring more qubits than are available on current devices. Here, we propose two new methods: first, we implement a multiple kernel method for data coming from multiple sources, and second, we propose to combine quantum chips to process larger data sets. The latter can be realized by splitting larger quantum circuits into smaller sub-circuits. We experimentally implement a multiple quantum kernel approach for different data sets on IBM quantum computers and benchmark their results.

DOI
10.23919/fusion49751.2022.9841330

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For quantum classification methods, the quantum kernel has a role in encoding the data set from its original low-dimensional real space into a high-dimensional quantum state space utilizing quantum circuits. Finding quantum kernels that provide an advantage in real-world data classification is a major challenge, especially when dealing with heterogeneous data or a large data set, requiring more qubits than are available on current devices. Here, we propose two new methods: first, we implement a multiple kernel method for data coming from multiple sources, and second, we propose to combine quantum chips to process larger data sets. The latter can be realized by splitting larger quantum circuits into smaller sub-circuits. We experimentally implement a multiple quantum kernel approach for different data sets on IBM quantum computers and benchmark their results.
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling gates scales quadratically with the dimension of the dataset and the number of qubits. In this work, we introduce a quantum feature map designed to handle high-dimensional data with a significantly reduced number of qubits and entangling operations. Our approach preserves essential data characteristics while promoting computational efficiency, as evidenced by extensive experiments on benchmark datasets that demonstrate a marked improvement in both accuracy and resource utilization when using our feature map as a kernel for characterization, as compared to state-of-the-art quantum feature maps. Our noisy simulation results, combined with lower resource requirements, highlight our map's ability to function within the constraints of noisy intermediate-scale quantum devices. Through numerical simulations and small-scale implementation on a superconducting circuit quantum computing platform, we demonstrate that our scheme performs on par or better than a set of classical algorithms for classification. While quantum kernels are typically stymied by exponential concentration, our approach is affected with a slower rate with respect to both the number of qubits and features, which allows practical applications to remain within reach. Our findings herald a promising avenue for the practical implementation of quantum machine learning algorithms on near future quantum computing platforms.
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements to gain a quadratic speedup in computation time and quickly process large datasets. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. We demonstrate the advantages of our methods by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our approach is exceptionally robust to noise via a complementary error mitigation scheme. Using currently available quantum computers, the MNIST database can be processed within 220 hours instead of 10 years which opens up industrial applications of quantum machine learning.
Quantum kernels map data to higher dimensions for classification and have been shown to have an advantage over classical methods. In our work, we generalize recent results in binary quantum kernels to multivalued logic by using higher dimensional entanglement to create a qudit memory and show that the use of qudits offers advantages in terms of quantum memory representation as well as enhanced resolution in the outcome of the kernel calculation. Our method is not only capable of finding the kernel inner product of higher dimensional data but can also efficiently and concurrently compute multiple instances of quantum kernel computations in linear time. We discuss how this method increases efficiency and resolution for various distance-based classifiers that require large datasets when accomplished with higher-dimensioned quantum data encodings. We provide experimental results of our qudit kernel calculations with different data encoding methods through the use of a higher-dimensioned quantum computation simulator.
Abstract Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements. The quantum computation time scales linearly with dataset size and quadratic for classical post-processing. While our method scales in general exponentially in qubit number, we gain a substantial speed-up when running on intermediate-sized quantum computers. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. Our approach is robust to noise via a cost-free error mitigation scheme. We demonstrate the advantages of our methods for noisy quantum computers by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our method enables benchmarking of quantum machine learning algorithms with large datasets on currently available quantum computers.
Quantum kernel techniques aim to leverage quantum computational capabilities on social data. However, their application to natural language processing tasks faces formidable obstacles, such as extreme dimensionality reduction (D=384→k=8), concentration of measure in quantum feature spaces, and the lack of theoretical understanding of when quantum advantages occur in kernel-based text classification. Filling this gap, we provide a comprehensive study of quantum kernels for text classification that addresses three major challenges in existing studies: general data compression approaches that ignore class structure, the lack of a predictive diagnostic toolkit, and overlooked approaches for handling concentration effects. Our main contributions include a supervised contrastive data compression approach with theoretical guarantees of kernel alignment, a five-diagnostic toolkit connecting theoretical insights with practical performance, the discovery of a small-data regime (n≤200) in which quantum methods perform comparably to classical approaches, and a transparent demonstration that quantum kernels require carefully designed settings to remain competitive with classical counterparts. Across four datasets, evaluated using five random seeds and exact paired statistical testing, we observe that quantum projected kernels achieve an accuracy of 84.5% compared to 85.1% for the classical RBF kernel (p>0.05, not statistically significant) under supervised compression settings. However, quantum methods lag behind by approximately 2%–4% at larger scales due to concentration effects, reflected in reduced off-diagonal kernel variance (0.003 vs. 0.025).
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, necessitates effective strategies to compress and embed large-scale real-world data like images into the constrained capacities of existing quantum devices or simulators. To this end, we propose Quantum Generator Kernels (QGKs), a generator-based approach to quantum kernels, comprising a set of Variational Generator Groups (VGGs) that merge universal generators into a parameterizable operator, ensuring scalable coverage of the available quantum space. Thereby, we address shortcomings of current leading strategies employing hybrid architectures, which might prevent exploiting quantum computing's full potential due to fixed intermediate embedding processes. To optimize the kernel alignment to the target domain, we train a weight vector to parameterize the projection of the VGGs in the current data context. Our empirical results demonstrate superior projection and classification capabilities of the QGK compared to state-of-the-art quantum and classical kernel approaches and show its potential to serve as a versatile framework for various QML applications.