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BRIDG-Q: Barren-Plateau-Resilient Initialisation with Data-Aware LLM-Generated Quantum Circuits

Ngoc Nhi Nguyen, Thai T Vu, John Le, Hoa Khanh Dam, Dung Hoang Duong, Dinh Thai Hoang

Abstract

Quantum circuit initialisation is a key bottleneck in variational quantum algorithms (VQAs), strongly impacting optimisation stability and convergence. Recent work shows that large language models (LLMs) can synthesise high-quality variational circuit architectures, but their continuous parameter predictions are unreliable. Conversely, data-driven initialisation methods such as BEINIT improve trainability via problem-adaptive priors, yet assume fixed ansatz templates and ignore generative circuit structure. We propose BRIDG-Q (Barren-Plateau-Resilient Initialisation with Data-Aware LLM-Generated Quantum Circuits), a neuro-symbolic pipeline that bridges this gap by coupling LLM-generated circuit architectures with empirical-Bayes parameter initialisation. BRIDG-Q uses AgentQ to generate problem-conditioned circuit topologies, removes generated parameters, and injects data-informed parameter initialisations to mitigate barren plateau effects. Evaluations on graph optimisation benchmarks using residual energy gap and convergence metrics show improved optimisation robustness, indicating that data-driven initialisation remains effective even for LLM-generated circuits, with oracle per-instance selection achieving approximately a 10% reduction in final residual energy.

BRIDG-Q: Barren-Plateau-Resilient Initialisation with Data-Aware LLM-Generated Quantum Circuits

Abstract

Quantum circuit initialisation is a key bottleneck in variational quantum algorithms (VQAs), strongly impacting optimisation stability and convergence. Recent work shows that large language models (LLMs) can synthesise high-quality variational circuit architectures, but their continuous parameter predictions are unreliable. Conversely, data-driven initialisation methods such as BEINIT improve trainability via problem-adaptive priors, yet assume fixed ansatz templates and ignore generative circuit structure. We propose BRIDG-Q (Barren-Plateau-Resilient Initialisation with Data-Aware LLM-Generated Quantum Circuits), a neuro-symbolic pipeline that bridges this gap by coupling LLM-generated circuit architectures with empirical-Bayes parameter initialisation. BRIDG-Q uses AgentQ to generate problem-conditioned circuit topologies, removes generated parameters, and injects data-informed parameter initialisations to mitigate barren plateau effects. Evaluations on graph optimisation benchmarks using residual energy gap and convergence metrics show improved optimisation robustness, indicating that data-driven initialisation remains effective even for LLM-generated circuits, with oracle per-instance selection achieving approximately a 10% reduction in final residual energy.
Paper Structure (40 sections, 6 equations, 2 figures, 2 tables, 1 algorithm)

This paper contains 40 sections, 6 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Barren plateaus and parameter initialisation.
  4. Empirical-Bayes initialisation.
  5. LLM-based circuit generation.
  6. Methodology: The BRIDG-Q Framework
  7. Architectural Overview
  8. Illustrative example: Max-Cut.
  9. Data-Driven Priors: The BEINIT Formulation
  10. Feature extraction.
  11. Beta distribution via MLE.
  12. Initialisation variants.
  13. $\text{BRIDG-Q}^{\beta\text{--stratified}}$: Gate-Aware Initialisation
  14. Core idea.
  15. Algorithmic procedure.
  16. ...and 25 more sections

Figures (2)

  • Figure 1: Overview of the BRIDG-Q neuro-symbolic pipeline for variational quantum optimisation. Figure created with assistance from Gemini 3 and edited by the authors.
  • Figure 2: Energy-gap trajectories for a representative problem instance (Sample 76). The plot shows the evolution of the absolute energy gap over optimisation iterations for different initialisation strategies. Beta-based methods ($\text{BRIDG-Q}^{\beta\text{--pure}}$, $\text{BRIDG-Q}^{\beta\text{--mixture}}$, and $\text{BRIDG-Q}^{\beta\text{--stratified}}$) exhibit slower initial convergence but continue to reduce the energy gap beyond the point where standard baselines (AgentQ, random, uniform) stagnate. In particular, $\text{BRIDG-Q}^{\beta\text{--stratified}}$ achieves the lowest final gap for this instance