Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.03291

Comprehensive Numerical Studies of Barren Plateau and Overparametrization in Variational Quantum Algorithm

Himuro Hashimoto, Akio Nakabayashi, Lento Nagano, Yutaro Iiyama, Ryu Sawada, Junichi Tanaka, Koji Terashi

quant-phcond-mat.str-elSubmitted Feb 3, 2026• Announced Feb 4, 2026• 0 citations
arXivHTMLPDF

Abstract

The variational quantum algorithm (VQA) with a parametrized quantum circuit is widely applicable to near-term quantum computing, but its fundamental issues that limit optimization performance have been reported in the literature. For example, VQA optimization often suffers from vanishing gradients called barren plateau (BP) and the presence of local minima in the landscape of the cost function. Numerical studies have shown that the trap in local minima is significantly reduced when the circuit is overparametrized (OP), where the number of parameters exceeds a certain threshold. Theoretical understanding of the BP and OP phenomena has advanced over the past years, however, comprehensive studies of both effects in the same setting are not fully covered in the literature. In this paper, we perform a comprehensive numerical study in VQA, quantitatively evaluating the impacts of BP and OP and their interplay on the optimization of a variational quantum circuit, using concrete implementations of one-dimensional transverse and longitudinal field quantum Ising model. The numerical results are compared with the theoretical diagnostics of BP and OP phenomena. The framework presented in this paper will provide a guiding principle for designing VQA algorithms and ansatzes with theoretical support for behaviors of parameter optimization in practical settings.

Comments
16 pages, 15 figures

Related papers

Enhancing variational quantum circuit training: an improved neural network approach for barren plateau mitigation

Yi Zhu, Yanying Liang, Haozhen Situ

Abstract Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. However, the training of variational quantum circuits (VQCs) is susceptible to a phenomenon known as barren plateaus (BPs). Various approaches have been proposed to mitigate this issue, such as using neural networks to generate VQC parameters. In this paper, we improve the NN-based BP mitigation approach by refining the neural network architecture and extend its applicability to a more generalized scenario that includes random quantum inputs and VQC structures. We evaluate the effectiveness of the approach by comparing the convergence speed before and after it is utilized. Furthermore, we give an explanation for the effectiveness of the NN-based BP mitigation approach by utilizing a loss landscape visualization technique and the expressibility metric of VQC. The smoothness of the loss landscape offers an intuitive insight into the approach’s utility, while the reduction in expressibility accounts for the enhanced trainability. Our research highlights the universal applicability of the NN-based BP mitigation approach, underscoring its potential to drive progress in the development of VQAs across diverse domains.

arXiv:2411.09226•Physica Scripta•Jul 16, 2025•6 citations

Breaking Through Barren Plateaus: Reinforcement Learning Initializations for Deep Variational Quantum Circuits

Yifeng Peng, Xinyi Li, Zhemin Zhang +3 more

Variational Quantum Algorithms (VQAs) have gained prominence as a viable framework for exploiting near-term quantum devices in applications ranging from optimization and chemistry simulation to machine learning. However, the effectiveness of VQAs is often constrained by the so-called barren plateau problem, wherein gradients diminish exponentially as system size or circuit depth increases, thereby hindering training. In this work, we propose a reinforcement learning (RL)-based initialization strategy to alleviate the barren plateau issue by reshaping the initial parameter landscape to avoid regions prone to vanishing gradients. In particular, we explore several RL algorithms (Deterministic Policy Gradient, Soft ActorCritic, and Proximal Policy Optimization, etc.) to generate the circuit parameters (treated as “actions”) that minimize the VQAs cost function before standard gradient-based optimization. By pre-training with RL in this manner, subsequent optimization using methods such as gradient descent or Adam proceeds from a more favorable initial state. Extensive numerical experiments under various noise conditions and tasks consistently demonstrate that the RL-based initialization method significantly enhances both convergence speed and final solution quality. Moreover, comparisons among different RL algorithms highlight that multiple approaches can achieve comparable performance gains, underscoring the flexibility and robustness of our method. These findings shed light on a promising avenue for integrating machine learning techniques into quantum algorithm design, offering insights into how RL-driven parameter initialization can accelerate the scalability and practical deployment of VQAs. Opening up a promising path for the research community in machine learning for quantum, especially barren plateau problems in VQAs.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•5 citations

On barren plateaus and cost function locality in variational quantum algorithms

A V Uvarov, Jacob Biamonte

Abstract Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in sufficiently expressive parametrized quantum circuits. It has been established that the onset of a barren plateau regime depends on the cost function, although the particular behavior has been demonstrated only for certain classes of cost functions. Here we derive a lower bound on the variance of the gradient, which depends mainly on the width of the circuit causal cone of each term in the Pauli decomposition of the cost function. Our result further clarifies the conditions under which barren plateaus can occur.

arXiv:2011.10530•Journal of Physics A Mathematical and Theoretical•Apr 22, 2021•126 citations

Escaping Barren Plateau: Co-Exploration of Quantum Circuit Parameters and Architectures

Yipei Liu, Yuhong Song, Li, Jinyang +4 more

Barren plateaus (BP), characterized by exponentially vanishing gradients that hinder the training of variational quantum circuits (VQC), present a pervasive and critical challenge in applying variational quantum algorithms to real-world applications. It is widely recognized that the BP problem becomes more pronounced with an increase in the number of parameters. This work demonstrates that the BP problem manifests at different scales depending on the specific application, highlighting the absence of a universal VQC ansatz capable of resolving the BP issue across all applications. Consequently, there is an imminent need for an automated tool to design and optimize VQC architectures tailored to specific applications. To close the gap, this paper takes Variational Quantum Eigensolvers (VQEs) as a vehicle, and we propose a novel quantum circuit parameter and architecture co-exploration framework, namely AntiBP. Experimental results demonstrate that AntiBP effectively avoids the BP issue for circuits that are not under-parameterized in noise-free environments. Furthermore, AntiBP significantly outperforms baseline VQEs in noisy environments.

arXiv:2501.13275•Jan 22, 2025•0 citations

Fundamental limitations on optimization in variational quantum algorithms

Hao-Kai Zhang, Chengkai Zhu, Geng Liu +1 more

Exploring quantum applications of near-term quantum devices is a rapidly growing field of quantum information science with both theoretical and practical interests. A leading paradigm to establish such near-term quantum applications is variational quantum algorithms (VQAs). These algorithms use a classical optimizer to train a parameterized quantum circuit to accomplish certain tasks, where the circuits are usually randomly initialized. In this work, we prove that for a broad class of such random circuits, the variation range of the cost function via adjusting any local quantum gate within the circuit vanishes exponentially in the number of qubits with a high probability. This result can unify the restrictions on gradient-based and gradient-free optimizations in a natural manner and reveal extra harsh constraints on the training landscapes of VQAs. Hence a fundamental limitation on the trainability of VQAs is unraveled, indicating the essential mechanism of the optimization hardness in the Hilbert space with exponential dimension. We further showcase the validity of our results with numerical simulations of representative VQAs. We believe that these results would deepen our understanding of the scalability of VQAs and shed light on the search for near-term quantum applications with advantages.

arXiv:2205.05056•May 10, 2022•3 citations

Batched Line Search Strategy for Navigating through Barren Plateaus in Quantum Circuit Training

Jakab Nádori, Gregory Morse, Barna Fülöp Villám +3 more

Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization loop. However, they often encounter challenges attributed to the exponentially diminishing gradient components, known as the barren plateau (BP) problem. This work introduces a novel optimization approach designed to alleviate the adverse effects of BPs during circuit training. In contrast to conventional gradient descent methods with a small learning parameter, our approach relies on making a finite hops along the search direction determined on a randomly chosen subsets of the free parameters. The optimization search direction, together with the range of the search, is determined by the distant features of the cost-function landscape. This enables the optimization path to navigate around barren plateaus without the need for external control mechanisms. We have successfully applied our optimization strategy to quantum circuits comprising 21 qubits and 15000 entangling gates, demonstrating robust resistance against BPs. Additionally, we have extended our optimization strategy by incorporating an evolutionary selection framework, enhancing its ability to avoid local minima in the landscape. The modified algorithm has been successfully utilized in quantum gate synthesis applications, showcasing a significantly improved efficiency in generating highly compressed quantum circuits compared to traditional gradient-based optimization approaches.

arXiv:2402.05227•Quantum•Aug 29, 2025•1 citation
The variational quantum algorithm (VQA) with a parametrized quantum circuit is widely applicable to near-term quantum computing, but its fundamental issues that limit optimization performance have been reported in the literature. For example, VQA optimization often suffers from vanishing gradients called barren plateau (BP) and the presence of local minima in the landscape of the cost function. Numerical studies have shown that the trap in local minima is significantly reduced when the circuit is overparametrized (OP), where the number of parameters exceeds a certain threshold. Theoretical understanding of the BP and OP phenomena has advanced over the past years, however, comprehensive studies of both effects in the same setting are not fully covered in the literature. In this paper, we perform a comprehensive numerical study in VQA, quantitatively evaluating the impacts of BP and OP and their interplay on the optimization of a variational quantum circuit, using concrete implementations of one-dimensional transverse and longitudinal field quantum Ising model. The numerical results are compared with the theoretical diagnostics of BP and OP phenomena. The framework presented in this paper will provide a guiding principle for designing VQA algorithms and ansatzes with theoretical support for behaviors of parameter optimization in practical settings.
Abstract Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. However, the training of variational quantum circuits (VQCs) is susceptible to a phenomenon known as barren plateaus (BPs). Various approaches have been proposed to mitigate this issue, such as using neural networks to generate VQC parameters. In this paper, we improve the NN-based BP mitigation approach by refining the neural network architecture and extend its applicability to a more generalized scenario that includes random quantum inputs and VQC structures. We evaluate the effectiveness of the approach by comparing the convergence speed before and after it is utilized. Furthermore, we give an explanation for the effectiveness of the NN-based BP mitigation approach by utilizing a loss landscape visualization technique and the expressibility metric of VQC. The smoothness of the loss landscape offers an intuitive insight into the approach’s utility, while the reduction in expressibility accounts for the enhanced trainability. Our research highlights the universal applicability of the NN-based BP mitigation approach, underscoring its potential to drive progress in the development of VQAs across diverse domains.
Variational Quantum Algorithms (VQAs) have gained prominence as a viable framework for exploiting near-term quantum devices in applications ranging from optimization and chemistry simulation to machine learning. However, the effectiveness of VQAs is often constrained by the so-called barren plateau problem, wherein gradients diminish exponentially as system size or circuit depth increases, thereby hindering training. In this work, we propose a reinforcement learning (RL)-based initialization strategy to alleviate the barren plateau issue by reshaping the initial parameter landscape to avoid regions prone to vanishing gradients. In particular, we explore several RL algorithms (Deterministic Policy Gradient, Soft ActorCritic, and Proximal Policy Optimization, etc.) to generate the circuit parameters (treated as “actions”) that minimize the VQAs cost function before standard gradient-based optimization. By pre-training with RL in this manner, subsequent optimization using methods such as gradient descent or Adam proceeds from a more favorable initial state. Extensive numerical experiments under various noise conditions and tasks consistently demonstrate that the RL-based initialization method significantly enhances both convergence speed and final solution quality. Moreover, comparisons among different RL algorithms highlight that multiple approaches can achieve comparable performance gains, underscoring the flexibility and robustness of our method. These findings shed light on a promising avenue for integrating machine learning techniques into quantum algorithm design, offering insights into how RL-driven parameter initialization can accelerate the scalability and practical deployment of VQAs. Opening up a promising path for the research community in machine learning for quantum, especially barren plateau problems in VQAs.
Abstract Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in sufficiently expressive parametrized quantum circuits. It has been established that the onset of a barren plateau regime depends on the cost function, although the particular behavior has been demonstrated only for certain classes of cost functions. Here we derive a lower bound on the variance of the gradient, which depends mainly on the width of the circuit causal cone of each term in the Pauli decomposition of the cost function. Our result further clarifies the conditions under which barren plateaus can occur.
Barren plateaus (BP), characterized by exponentially vanishing gradients that hinder the training of variational quantum circuits (VQC), present a pervasive and critical challenge in applying variational quantum algorithms to real-world applications. It is widely recognized that the BP problem becomes more pronounced with an increase in the number of parameters. This work demonstrates that the BP problem manifests at different scales depending on the specific application, highlighting the absence of a universal VQC ansatz capable of resolving the BP issue across all applications. Consequently, there is an imminent need for an automated tool to design and optimize VQC architectures tailored to specific applications. To close the gap, this paper takes Variational Quantum Eigensolvers (VQEs) as a vehicle, and we propose a novel quantum circuit parameter and architecture co-exploration framework, namely AntiBP. Experimental results demonstrate that AntiBP effectively avoids the BP issue for circuits that are not under-parameterized in noise-free environments. Furthermore, AntiBP significantly outperforms baseline VQEs in noisy environments.
Exploring quantum applications of near-term quantum devices is a rapidly growing field of quantum information science with both theoretical and practical interests. A leading paradigm to establish such near-term quantum applications is variational quantum algorithms (VQAs). These algorithms use a classical optimizer to train a parameterized quantum circuit to accomplish certain tasks, where the circuits are usually randomly initialized. In this work, we prove that for a broad class of such random circuits, the variation range of the cost function via adjusting any local quantum gate within the circuit vanishes exponentially in the number of qubits with a high probability. This result can unify the restrictions on gradient-based and gradient-free optimizations in a natural manner and reveal extra harsh constraints on the training landscapes of VQAs. Hence a fundamental limitation on the trainability of VQAs is unraveled, indicating the essential mechanism of the optimization hardness in the Hilbert space with exponential dimension. We further showcase the validity of our results with numerical simulations of representative VQAs. We believe that these results would deepen our understanding of the scalability of VQAs and shed light on the search for near-term quantum applications with advantages.
Variational quantum algorithms are viewed as promising candidates for demonstrating quantum advantage on near-term devices. These approaches typically involve the training of parameterized quantum circuits through a classical optimization loop. However, they often encounter challenges attributed to the exponentially diminishing gradient components, known as the barren plateau (BP) problem. This work introduces a novel optimization approach designed to alleviate the adverse effects of BPs during circuit training. In contrast to conventional gradient descent methods with a small learning parameter, our approach relies on making a finite hops along the search direction determined on a randomly chosen subsets of the free parameters. The optimization search direction, together with the range of the search, is determined by the distant features of the cost-function landscape. This enables the optimization path to navigate around barren plateaus without the need for external control mechanisms. We have successfully applied our optimization strategy to quantum circuits comprising 21 qubits and 15000 entangling gates, demonstrating robust resistance against BPs. Additionally, we have extended our optimization strategy by incorporating an evolutionary selection framework, enhancing its ability to avoid local minima in the landscape. The modified algorithm has been successfully utilized in quantum gate synthesis applications, showcasing a significantly improved efficiency in generating highly compressed quantum circuits compared to traditional gradient-based optimization approaches.