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Q-Fusion: Diffusing Quantum Circuits

Collin Beaudoin, Swaroop Ghosh

TL;DR

The paper tackles the challenge of designing quantum circuits for NISQ devices by introducing Q-Fusion, a diffusion-model-based Quantum Architecture Search that operates on graph representations of circuits (LayerDAG). It trains a three-layer diffusion model to generate valid circuit DAGs and demonstrates 100% validity in both non-parametric and parametric circuit generation, with meaningful functionality dependent on gate sets and circuit size. The approach leverages a density-matrix–based label to guide learning, but faces limitations from the exponential scaling of density matrices with qubit count and from data scarcity, motivating future enhancements such as quantum-aware optimization and hardware-based evaluation. Overall, diffusion-based QAS presents a promising direction for automated quantum circuit design, potentially accelerating quantum machine learning and other quantum technologies.

Abstract

Quantum computing holds great potential for solving socially relevant and computationally complex problems. Furthermore, quantum machine learning (QML) promises to rapidly improve our current machine learning capabilities. However, current noisy intermediate-scale quantum (NISQ) devices are constrained by limitations in the number of qubits and gate counts, which hinder their full capabilities. Furthermore, the design of quantum algorithms remains a laborious task, requiring significant domain expertise and time. Quantum Architecture Search (QAS) aims to streamline this process by automatically generating novel quantum circuits, reducing the need for manual intervention. In this paper, we propose a diffusion-based algorithm leveraging the LayerDAG framework to generate new quantum circuits. This method contrasts with other approaches that utilize large language models (LLMs), reinforcement learning (RL), variational autoencoders (VAE), and similar techniques. Our results demonstrate that the proposed model consistently generates 100% valid quantum circuit outputs.

Q-Fusion: Diffusing Quantum Circuits

TL;DR

The paper tackles the challenge of designing quantum circuits for NISQ devices by introducing Q-Fusion, a diffusion-model-based Quantum Architecture Search that operates on graph representations of circuits (LayerDAG). It trains a three-layer diffusion model to generate valid circuit DAGs and demonstrates 100% validity in both non-parametric and parametric circuit generation, with meaningful functionality dependent on gate sets and circuit size. The approach leverages a density-matrix–based label to guide learning, but faces limitations from the exponential scaling of density matrices with qubit count and from data scarcity, motivating future enhancements such as quantum-aware optimization and hardware-based evaluation. Overall, diffusion-based QAS presents a promising direction for automated quantum circuit design, potentially accelerating quantum machine learning and other quantum technologies.

Abstract

Quantum computing holds great potential for solving socially relevant and computationally complex problems. Furthermore, quantum machine learning (QML) promises to rapidly improve our current machine learning capabilities. However, current noisy intermediate-scale quantum (NISQ) devices are constrained by limitations in the number of qubits and gate counts, which hinder their full capabilities. Furthermore, the design of quantum algorithms remains a laborious task, requiring significant domain expertise and time. Quantum Architecture Search (QAS) aims to streamline this process by automatically generating novel quantum circuits, reducing the need for manual intervention. In this paper, we propose a diffusion-based algorithm leveraging the LayerDAG framework to generate new quantum circuits. This method contrasts with other approaches that utilize large language models (LLMs), reinforcement learning (RL), variational autoencoders (VAE), and similar techniques. Our results demonstrate that the proposed model consistently generates 100% valid quantum circuit outputs.
Paper Structure (28 sections, 4 figures, 2 tables)

This paper contains 28 sections, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Fundamentals of Quantum
  4. Qubits
  5. Quantum Gates
  6. Diffusion Neural Networks
  7. Quantum Architecture Search
  8. Q-Fusion: Approach
  9. Approach
  10. Training
  11. Sampling
  12. Model Updates
  13. Graph Generation
  14. Wire Information
  15. Model Information
  16. ...and 13 more sections

Figures (4)

  • Figure 1: Sample of the diffusion process. The top shows how an image structure is destroyed via noise over several steps. The bottom shows how structure is recreated using a model.
  • Figure 2: Overview of Q-Fusion process for generating quantum circuits. The top image represents the training process of the diffusion model. The bottom image displays the sampling method used to create new circuits from the trained diffusion model.
  • Figure 3: Underlying structure of 3 layered diffusion model.
  • Figure 4: Example Quantum Circuit produced by Q-Fusion for the 2 qubit 8 gate trained model