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Evidential Quantum Vertical Federated Learning

Hao Luo, Zhiyuan Zhai, Qianli Zhou, Jun Qi, Yong Deng, Xin Wang

Abstract

Quantum federated learning (QFL) has recently emerged as a promising paradigm for privacy-preserving collaborative learning, yet most existing studies focus on horizontal federated learning and ignore the vertical federated learning (VFL), where parties hold complementary features of aligned samples. In this work, we propose Evidential Quantum Vertical Federated Learning (eviQVFL), a VFL-tailored QFL framework that employs a hybrid classical-quantum architecture for party-side feature processing, mapping local features into a quantum state. To preserve privacy and avoid information loss, party-side output states are directly transmitted to the server via quantum teleportation, and the server fuses the received quantum states with a non-parametric evidential fusion circuit grounded in evidence theory, followed by measurement-based inference. Extensive simulations on image classification and other real-world datasets demonstrate that eviQVFL consistently achieves higher classification accuracy than other classical and quantum baselines under comparable parameter budgets. Both empirical observations and theoretical analysis indicate that eviQVFL achieve less approximation error with limited quantum resources, while maintaining training stability and offering stronger feature privacy.

Evidential Quantum Vertical Federated Learning

Abstract

Quantum federated learning (QFL) has recently emerged as a promising paradigm for privacy-preserving collaborative learning, yet most existing studies focus on horizontal federated learning and ignore the vertical federated learning (VFL), where parties hold complementary features of aligned samples. In this work, we propose Evidential Quantum Vertical Federated Learning (eviQVFL), a VFL-tailored QFL framework that employs a hybrid classical-quantum architecture for party-side feature processing, mapping local features into a quantum state. To preserve privacy and avoid information loss, party-side output states are directly transmitted to the server via quantum teleportation, and the server fuses the received quantum states with a non-parametric evidential fusion circuit grounded in evidence theory, followed by measurement-based inference. Extensive simulations on image classification and other real-world datasets demonstrate that eviQVFL consistently achieves higher classification accuracy than other classical and quantum baselines under comparable parameter budgets. Both empirical observations and theoretical analysis indicate that eviQVFL achieve less approximation error with limited quantum resources, while maintaining training stability and offering stronger feature privacy.
Paper Structure (20 sections, 2 theorems, 29 equations, 14 figures, 3 tables, 1 algorithm)

This paper contains 20 sections, 2 theorems, 29 equations, 14 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Classical vertical federated learning
  4. Quantum computing
  5. Evidence theory and its quantum equivalence
  6. The eviQVFL framework
  7. The overall quantum VFL framework
  8. Party-side feature processing
  9. Dimension reduction by TTN
  10. Angle encoding
  11. VQC
  12. Quantum teleportation
  13. Server-side evidential aggregating
  14. Experimental Results and Analysis
  15. Experiment Setup
  16. ...and 5 more sections

Key Result

Proposition 1

In a $C$ class classification task, the CE loss for models with the quantum measurement as the output has a lower bound: $\mathcal{L}\geq\ln(C+e-1)-1$. Proof. Let $\hat{\mathbf{y}}=[\hat{y}_i(1),\ldots,\hat{y}_i(C)]$ with $\hat{y}_i(c)\in [0,1]$ be the output logits. Without loss of generality, ass $\Box$ However, the classical models output unbounded real-valued logits, for which the loss is onl

Figures (14)

  • Figure 1: The comparison between HFL and VFL.
  • Figure 2: The quantum circuit of preparing EPR pair.
  • Figure 3: Overall architecture of the proposed quantum vertical VFL framework. Solid lines denote classical communication, dashed lines denote quantum communication. Black arrows indicate the forward-propagation flow of quantum states or classical signals, while red arrows indicate the classical update according to the gradients.
  • Figure 4: Tensor Train Network (TTN) acting on an input represented in Tensor Train (TT) form. The top row shows TT cores $\mathcal{X}^{(l)} \in \mathbb{R}^{R^{\mathcal{X}}_{l-1} \times P_l \times R^{\mathcal{X}}_{l}}$ for $l=1,\dots,L$. The bottom row shows the TT-operator cores $\mathcal{W}^{(l)} \in \mathbb{R}^{R^{\mathcal{W}}_{l-1} \times P_l \times Q_l \times R^{\mathcal{W}}_{l}}$. Each pair of corresponding cores is contracted along the shared input mode $P_l$, producing an output tensor of size $Q_1 \times \cdots \times Q_L$. Vertical legs denote physical modes ($P_l$, $Q_l$); horizontal legs denote TT bond dimensions $R^{\mathcal{X}}_{l}$ and $R^{\mathcal{W}}_{l}$ (with boundary ranks $R^{\mathcal{X}}_{0}=R^{\mathcal{X}}_{L}=R^{\mathcal{W}}_{0}=R^{\mathcal{W}}_{L}=1$).
  • Figure 5: The quantum circuit of the VQC structure employed.
  • ...and 9 more figures

Theorems & Definitions (2)

  • Proposition 1
  • Proposition 2