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Escaping Barren Plateaus in Variational Quantum Algorithms Using Negative Learning Rate in Quantum Internet of Things

Ratun Rahman, Dinh C. Nguyen

TL;DR

The paper tackles the problem of barren plateaus in variational quantum algorithms deployed on resource-constrained QIoT devices. It introduces Negative Learning Rate (NLR) training, which intermittently ascends the cost landscape when a descent would worsen the loss, thereby enhancing exploration and gradient flow. Theoretical analysis links NLR to diffusion-like behavior in parameter space and validates its effectiveness through simulations on synthetic and public datasets, showing reduced training loss and stronger gradients. This optimizer-level approach offers a practical pathway to robust, on-device quantum learning for edge-enabled quantum sensing and inference.

Abstract

Variational Quantum Algorithms (VQAs) are becoming the primary computational primitive for next-generation quantum computers, particularly those embedded as resource-constrained accelerators in the emerging Quantum Internet of Things (QIoT). However, under such device-constrained execution conditions, the scalability of learning is severely limited by barren plateaus, where gradients collapse to zero and training stalls. This poses a practical challenge to delivering VQA-enabled intelligence on QIoT endpoints, which often have few qubits, constrained shot budgets, and strict latency requirements. In this paper, we present a novel approach for escaping barren plateaus by including negative learning rates into the optimization process in QIoT devices. Our method introduces controlled instability into model training by switching between positive and negative learning phases, allowing recovery of significant gradients and exploring flatter areas in the loss landscape. We theoretically evaluate the effect of negative learning on gradient variance and propose conditions under which it helps escape from barren zones. The experimental findings on typical VQA benchmarks show consistent improvements in both convergence and simulation results over traditional optimizers. By escaping barren plateaus, our approach leads to a novel pathway for robust optimization in quantum-classical hybrid models.

Escaping Barren Plateaus in Variational Quantum Algorithms Using Negative Learning Rate in Quantum Internet of Things

TL;DR

The paper tackles the problem of barren plateaus in variational quantum algorithms deployed on resource-constrained QIoT devices. It introduces Negative Learning Rate (NLR) training, which intermittently ascends the cost landscape when a descent would worsen the loss, thereby enhancing exploration and gradient flow. Theoretical analysis links NLR to diffusion-like behavior in parameter space and validates its effectiveness through simulations on synthetic and public datasets, showing reduced training loss and stronger gradients. This optimizer-level approach offers a practical pathway to robust, on-device quantum learning for edge-enabled quantum sensing and inference.

Abstract

Variational Quantum Algorithms (VQAs) are becoming the primary computational primitive for next-generation quantum computers, particularly those embedded as resource-constrained accelerators in the emerging Quantum Internet of Things (QIoT). However, under such device-constrained execution conditions, the scalability of learning is severely limited by barren plateaus, where gradients collapse to zero and training stalls. This poses a practical challenge to delivering VQA-enabled intelligence on QIoT endpoints, which often have few qubits, constrained shot budgets, and strict latency requirements. In this paper, we present a novel approach for escaping barren plateaus by including negative learning rates into the optimization process in QIoT devices. Our method introduces controlled instability into model training by switching between positive and negative learning phases, allowing recovery of significant gradients and exploring flatter areas in the loss landscape. We theoretically evaluate the effect of negative learning on gradient variance and propose conditions under which it helps escape from barren zones. The experimental findings on typical VQA benchmarks show consistent improvements in both convergence and simulation results over traditional optimizers. By escaping barren plateaus, our approach leads to a novel pathway for robust optimization in quantum-classical hybrid models.

Paper Structure

This paper contains 18 sections, 4 theorems, 15 equations, 4 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related works
  3. Methods
  4. Quantum Machine Learning
  5. Negative Learning Rate Training
  6. Algorithm
  7. Theoretical Analysis
  8. Assumptions
  9. Technical Lemmas
  10. Diffusion in Barren Plateaus
  11. Post-Escape Behavior
  12. Experiments
  13. Quantum Model Architecture
  14. Dataset
  15. Hyperparameter Analysis
  16. ...and 3 more sections

Key Result

Lemma 1

For $\theta_t \in \mathcal{B}$ and a small $\eta$, the change of cost is: where $H_t=\nabla^2 C(\theta_t)$. The violation event $\mathcal{E}_t = \{C(\theta_t - \eta g_t) > C(\theta_t)\}$ happens approximately when In plateau areas, where $\|\nabla C(\theta_t)\| \leq \varepsilon \ll \sigma$, the first-order gradient signal is severely weak. The apparent cost variation may be impacted by both curv

Figures (4)

  • Figure 1: Visualization of a synthetic barren plateau. (a) shows the 3D cost surface with a cave structure centered at $(-2, -2)$, while (b) illustrates the corresponding gradient vanishing behavior.
  • Figure 2: Simulation results demonstrate that, in comparison to standard training, negative learning-rate training produces a far superior convergence trajectory—the loss continues decreasing, escaping early stagnation.
  • Figure 3: A comparison of the gradient norm $\|\nabla_\theta C(\theta)\|$ during training for standard optimization and negative learning rate training. The standard approach exhibits a fast decline of the gradient norm, signaling entry into a barren plateau, but the negative learning strategy retains greater gradient values with periodic recovery, allowing for successful exploration and escape from flat regions.
  • Figure 4: The effect of perturbation noise on final training loss. Small perturbations enhance escape from plateaus, but high noise amplitudes hinder convergence and increase losses.

Theorems & Definitions (6)

  • Lemma 1: Acceptance Test via Curvature
  • Lemma 2: Backtracking Cap under Violation
  • Theorem 1: Diffusion Ordering in Barren Plateaus
  • Remark 1: Exit-Time Scaling
  • Theorem 2: Post-Escape Stability
  • Remark 2