Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Q-RUN: Quantum-Inspired Data Re-uploading Networks

Wenbo Qiao, Shuaixian Wang, Peng Zhang, Yan Ming, Jiaming Zhao

TL;DR

<3-5 sentence high-level summary> Q-RUN introduces a quantum-inspired, data re-uploading network that transfers the Fourier-series expressivity of data re-uploading quantum circuits to classical neural networks, enabling high-frequency function fitting with far fewer parameters. By replacing or augmenting fully connected layers with a two-module design—Data Re-uploading and a lightweight Element-wise Observable Module—Q-RUN achieves strong performance across data modeling and predictive tasks, often outperforming state-of-the-art Fourier-based and standard baselines while using fewer parameters. The framework is shown to approximate DRQC behavior, excel in implicit representations, density estimation, and energy modeling, and provide robust parameter-efficient fine-tuning and transfer to vision and language tasks. This work demonstrates a practical pathway to harness quantum-inspired inductive biases in classical AI, with broad applicability and plug-and-play compatibility for existing architectures.

Abstract

Data re-uploading quantum circuits (DRQC) are a key approach to implementing quantum neural networks and have been shown to outperform classical neural networks in fitting high-frequency functions. However, their practical application is limited by the scalability of current quantum hardware. In this paper, we introduce the mathematical paradigm of DRQC into classical models by proposing a quantum-inspired data re-uploading network (Q-RUN), which retains the Fourier-expressive advantages of quantum models without any quantum hardware. Experimental results demonstrate that Q-RUN delivers superior performance across both data modeling and predictive modeling tasks. Compared to the fully connected layers and the state-of-the-art neural network layers, Q-RUN reduces model parameters while decreasing error by approximately one to three orders of magnitude on certain tasks. Notably, Q-RUN can serve as a drop-in replacement for standard fully connected layers, improving the performance of a wide range of neural architectures. This work illustrates how principles from quantum machine learning can guide the design of more expressive artificial intelligence.

Q-RUN: Quantum-Inspired Data Re-uploading Networks

TL;DR

<3-5 sentence high-level summary> Q-RUN introduces a quantum-inspired, data re-uploading network that transfers the Fourier-series expressivity of data re-uploading quantum circuits to classical neural networks, enabling high-frequency function fitting with far fewer parameters. By replacing or augmenting fully connected layers with a two-module design—Data Re-uploading and a lightweight Element-wise Observable Module—Q-RUN achieves strong performance across data modeling and predictive tasks, often outperforming state-of-the-art Fourier-based and standard baselines while using fewer parameters. The framework is shown to approximate DRQC behavior, excel in implicit representations, density estimation, and energy modeling, and provide robust parameter-efficient fine-tuning and transfer to vision and language tasks. This work demonstrates a practical pathway to harness quantum-inspired inductive biases in classical AI, with broad applicability and plug-and-play compatibility for existing architectures.

Abstract

Data re-uploading quantum circuits (DRQC) are a key approach to implementing quantum neural networks and have been shown to outperform classical neural networks in fitting high-frequency functions. However, their practical application is limited by the scalability of current quantum hardware. In this paper, we introduce the mathematical paradigm of DRQC into classical models by proposing a quantum-inspired data re-uploading network (Q-RUN), which retains the Fourier-expressive advantages of quantum models without any quantum hardware. Experimental results demonstrate that Q-RUN delivers superior performance across both data modeling and predictive modeling tasks. Compared to the fully connected layers and the state-of-the-art neural network layers, Q-RUN reduces model parameters while decreasing error by approximately one to three orders of magnitude on certain tasks. Notably, Q-RUN can serve as a drop-in replacement for standard fully connected layers, improving the performance of a wide range of neural architectures. This work illustrates how principles from quantum machine learning can guide the design of more expressive artificial intelligence.
Paper Structure (31 sections, 33 equations, 9 figures, 8 tables)

This paper contains 31 sections, 33 equations, 9 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Classical Neural Network
  4. Quantum Neural Network
  5. Preliminaries
  6. Data Re-uploading Quantum Circuit
  7. Methodology
  8. Theoretical Formulation of Q-RUN
  9. Relaxed Implementation of Q-RUN
  10. Data Re-uploading Module
  11. Element-wise Observable Module
  12. Experiments
  13. RQ1: Experiments on DRQC Approximation
  14. RQ2: Experiments on Data Modeling Tasks
  15. Implicit Representation
  16. ...and 16 more sections

Figures (9)

  • Figure 1: Comparison of classical and quantum neural networks. The underlines highlight the respective strengths of the two computational paradigms.
  • Figure 2: Q-RUN is situated within the related literature on variational quantum circuit–inspired neural networks.
  • Figure 3: Several variants of DRQC. (a) Generalized architecture. (b) Multi-qubit, single-layer encoding scheme. (c) Single-qubit, multi-layer encoding scheme. Schemes (b) and (c) are equivalent in expressive power.
  • Figure 4: The Q-RUN layer under relaxed implementation can replace fully connected layers of diverse architectures.
  • Figure 5: The internal structure of the Element-wise Observable Module.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Claim 1
  • Claim 2
  • proof : Sketch of Proof
  • proof : Proof