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Quantum-Enhanced Generative Models for Rare Event Prediction

M. Z. Haider, M. U. Ghouri, Tayyaba Noreen, M. Salman

TL;DR

Rare-event prediction is hindered by heavy-tailed distributions and mode collapse in classical generative models. The authors introduce Quantum-Enhanced Generative Model (QEGM), a hybrid quantum-classical framework that embeds a variational quantum circuit into a diffusion-style generative process and optimizes a tail-aware objective, aided by quantum randomness for diverse sampling. Key innovations include a tail-focused loss, a Quantum Variational Layer for rare-event encoding, and a hybrid training loop using backpropagation for classical parameters and the parameter-shift rule for quantum parameters, plus QRNG-based noise Injection. Empirical results on synthetic Gaussian mixtures and real-world datasets from finance, climate, and biology show substantial gains in tail fidelity, with tail KL divergence reduced by up to 50% and rare-event recall improved (e.g., from 0.62–0.74 up to 0.83–0.88), indicating strong potential for robust rare-event prediction in high-stakes applications.

Abstract

Rare events such as financial crashes, climate extremes, and biological anomalies are notoriously difficult to model due to their scarcity and heavy-tailed distributions. Classical deep generative models often struggle to capture these rare occurrences, either collapsing low-probability modes or producing poorly calibrated uncertainty estimates. In this work, we propose the Quantum-Enhanced Generative Model (QEGM), a hybrid classical-quantum framework that integrates deep latent-variable models with variational quantum circuits. The framework introduces two key innovations: (1) a hybrid loss function that jointly optimizes reconstruction fidelity and tail-aware likelihood, and (2) quantum randomness-driven noise injection to enhance sample diversity and mitigate mode collapse. Training proceeds via a hybrid loop where classical parameters are updated through backpropagation while quantum parameters are optimized using parameter-shift gradients. We evaluate QEGM on synthetic Gaussian mixtures and real-world datasets spanning finance, climate, and protein structure. Results demonstrate that QEGM reduces tail KL divergence by up to 50 percent compared to state-of-the-art baselines (GAN, VAE, Diffusion), while improving rare-event recall and coverage calibration. These findings highlight the potential of QEGM as a principled approach for rare-event prediction, offering robustness beyond what is achievable with purely classical methods.

Quantum-Enhanced Generative Models for Rare Event Prediction

TL;DR

Rare-event prediction is hindered by heavy-tailed distributions and mode collapse in classical generative models. The authors introduce Quantum-Enhanced Generative Model (QEGM), a hybrid quantum-classical framework that embeds a variational quantum circuit into a diffusion-style generative process and optimizes a tail-aware objective, aided by quantum randomness for diverse sampling. Key innovations include a tail-focused loss, a Quantum Variational Layer for rare-event encoding, and a hybrid training loop using backpropagation for classical parameters and the parameter-shift rule for quantum parameters, plus QRNG-based noise Injection. Empirical results on synthetic Gaussian mixtures and real-world datasets from finance, climate, and biology show substantial gains in tail fidelity, with tail KL divergence reduced by up to 50% and rare-event recall improved (e.g., from 0.62–0.74 up to 0.83–0.88), indicating strong potential for robust rare-event prediction in high-stakes applications.

Abstract

Rare events such as financial crashes, climate extremes, and biological anomalies are notoriously difficult to model due to their scarcity and heavy-tailed distributions. Classical deep generative models often struggle to capture these rare occurrences, either collapsing low-probability modes or producing poorly calibrated uncertainty estimates. In this work, we propose the Quantum-Enhanced Generative Model (QEGM), a hybrid classical-quantum framework that integrates deep latent-variable models with variational quantum circuits. The framework introduces two key innovations: (1) a hybrid loss function that jointly optimizes reconstruction fidelity and tail-aware likelihood, and (2) quantum randomness-driven noise injection to enhance sample diversity and mitigate mode collapse. Training proceeds via a hybrid loop where classical parameters are updated through backpropagation while quantum parameters are optimized using parameter-shift gradients. We evaluate QEGM on synthetic Gaussian mixtures and real-world datasets spanning finance, climate, and protein structure. Results demonstrate that QEGM reduces tail KL divergence by up to 50 percent compared to state-of-the-art baselines (GAN, VAE, Diffusion), while improving rare-event recall and coverage calibration. These findings highlight the potential of QEGM as a principled approach for rare-event prediction, offering robustness beyond what is achievable with purely classical methods.

Paper Structure

This paper contains 19 sections, 30 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Problem Formulation
  4. Proposed Framework: Quantum-Enhanced Generative Models (QEGM)
  5. Architecture Overview
  6. Quantum Variational Layer for Rare Event Encoding
  7. Hybrid Classical--Quantum Training Loop
  8. Noise Injection via Quantum Randomness
  9. Methodology
  10. Data Preparation and Rare Event Benchmark Datasets
  11. Quantum Circuit Design
  12. Training Strategy: Hybrid Backpropagation + Quantum Gradients
  13. Complexity Analysis
  14. Experimental Evaluation
  15. Experimental Setup and Baselines
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Real and fake data from generative modelsbelis2024quantum
  • Figure 2: Architecture of range-based sharding protocol.
  • Figure 3: Comparison of generative quality across baseline models (GAN, VAE, Diffusion) and the proposed QEGM. Lower FID indicates higher quality.
  • Figure 4: Evaluation of QEGM vs baselines: (a) rare-event recall and (b) FID vs epochs.
  • Figure 5: (a) Predictive-interval calibration—empirical vs. nominal coverage; (b) synthetic Gaussian-mixture density.