Distributed and Secure Kernel-Based Quantum Machine Learning

TL;DR

This work tackles secure, distributed kernel-based quantum machine learning by linking quantum data encodings to classical kernel functions through quantum feature maps. It introduces three quantum feature maps for polynomial, RBF, and Laplacian kernels and embeds them in a distributed, semi-honest architecture that uses quantum teleportation and a helper to securely compute kernel similarities. The authors provide theoretical proofs of the feature maps' correctness, analyze computational complexity, and validate the architecture on public datasets using the Qiskit Aer Simulator, showing competitive performance relative to centralized quantum methods and robustness to noise. The study lays groundwork for privacy-preserving, distributed quantum kernel learning and outlines future directions toward malicious-adversary resilience and expanded kernel mappings.

Abstract

Quantum computing promises to revolutionize machine learning, offering significant efficiency gains in tasks such as clustering and distance estimation. Additionally, it provides enhanced security through fundamental principles like the measurement postulate and the no-cloning theorem, enabling secure protocols such as quantum teleportation and quantum key distribution. While advancements in secure quantum machine learning are notable, the development of secure and distributed quantum analogues of kernel-based machine learning techniques remains underexplored. In this work, we present a novel approach for securely computing common kernels, including polynomial, radial basis function (RBF), and Laplacian kernels, when data is distributed, using quantum feature maps. Our methodology introduces a robust framework that leverages quantum teleportation to ensure secure and distributed kernel learning. The proposed architecture is validated using IBM's Qiskit Aer Simulator on various public datasets.

Figures (9)

• Figure 1: Visualization of our architecture consisting of a helper, a server, and multiple clients.
• Figure 2: Quantum circuit diagram associated with our secure and distributed quantum-based kernel computation architecture.
• Figure 3: Comparison of accuracy scores across different noise levels. The baseline includes centralized classical kernel computation and our distributed quantum kernel computation with no noise. We incrementally introduce noise, using depolarizing error at Level 1 and Level 2, to evaluate and report the corresponding accuracy loss.
• Figure 4: Accuracy of linear kernel-based SVM on a subset of the Digits dataset featuring 100 samples and 10 labels, compared against the number of shots run by the simulator.
• Figure : (a) RBF Kernel, $d=10$. Different curves correspond to various values of $\sigma$, with the x-axis showing the number of random features $D$ (and corresponding qubits, $\lceil \log_2(2D) \rceil$).

Theorems & Definitions (16)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof