Robust Decentralized Quantum Kernel Learning for Noisy and Adversarial Environment

TL;DR

This work tackles the challenge of quantum kernel learning in distributed, noisy, and potentially adversarial environments. It introduces Robust Decentralized Quantum Kernel Learning (RDQKL), which optimizes a kernel-alignment objective $L(D, m{ heta}) = -A(K_e(m{ heta}), K^*)$ using a decentralized protocol with a clipping-based robust aggregation to bound adversarial influence. The authors provide theoretical insights into consensus under heterogeneous noise and demonstrate empirically that RDQKL maintains high accuracy under depolarizing noise and resists adversarial data injections on synthetic and reduced real datasets. The framework enables scalable, secure quantum machine learning on near-term hardware with heterogeneous participants.

Abstract

This paper proposes a general decentralized framework for quantum kernel learning (QKL). It has robustness against quantum noise and can also be designed to defend adversarial information attacks forming a robust approach named RDQKL. We analyze the impact of noise on QKL and study the robustness of decentralized QKL to the noise. By integrating robust decentralized optimization techniques, our method is able to mitigate the impact of malicious data injections across multiple nodes. Experimental results demonstrate that our approach maintains high accuracy under noisy quantum operations and effectively counter adversarial modifications, offering a promising pathway towards the future practical, scalable and secure quantum machine learning (QML).

Figures (5)

• Figure 1: A schematic overview of the application scenario. Multiple quantum computing units (QU) collaborate on a shared machine learning task to accelerate the training or preserve the data privacy. In this open environment, certain nodes may suffer from high noise or malicious behavior, potentially sabotaging the training process.
• Figure 2: A quantum feature mapping circuit under noise with variational parameters. The circuit can be sequentially divided into a superposition layer, an embedding layer and a trainable parameter layer. The superposition layer applies Hardman gate to each qubit to build a superposition state. The embedding layer applies a z-axis rotation with an angle of $x_i$ to the $i^{th}$ qubit thereby embedding the information of $x$ into the working system. The trainable parameter layer includes the y-axis rotation applied to each qubit and a ring broadcast layer in order to create entanglement and broadcast information. Each quantum gate is followed by a depolarized noise channel.
• Figure 3: Quantum kernel alignment value during the training process under different noise intensities. The larger the quantum kernel alignment value, the better the quantum kernel distinguishes on the specific data set. The quantun circuit is described in A of Section \ref{['sec:experiments']}.
• Figure 4: The checkerboard data is within a 1x1-sized region, divided into a total of 16 checkerboard cells , each of which is a square of $0.25\times0.25$. Each cell contains Gaussian random data centered around the respective checkerboard. The checkerboard dataset is heterogeneously partitioned into a ring topology and Node $2$ is set as a high noise or malicious node.
• Figure 5: The MNIST dataset is reduced in dimension to a 1x1-sized region using an autoencoder. The encoder, which contains $4$ fully connected layers with gradually decreasing dimensions, maps them to a 2D representation, and the decoder, which contains 4 corresponding fully connected layers, attempts to reconstruct the original input data for digits 7 and 9 from this low-dimensional representation. The reduced-dimensional MNIST dataset is randomly divided into a fully connected topology and Node $2$ is set as a high noise or malicious node.