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.
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) are among the most promising algorithms in the era of noisy intermediate scale quantum devices. Such algorithms are constructed using a parametrization $U(\ensuremath{\theta}$) with a classical optimizer that updates the parameters $\ensuremath{\theta}$ in order to minimize a cost function C. For this task, in general the gradient descent method, or one of its variants, is used. This is a method where the circuit parameters are updated iteratively using the cost function gradient. However, several works in the literature have shown that this method suffers from a phenomenon known as the barren plateaus (BPs). In this paper, we propose a method to mitigate BPs. In general, the parameters $\ensuremath{\theta}$ used in the parametrization U are randomly generated. In our method they are obtained from a classical neural network (CNN). We show that this method, besides to being able to mitigate BPs during startup, is also able to mitigate the effect of BPs during the VQA training. In addition, we also show how this method behaves for different CNN architectures.
Parameterized quantum circuits (PQCs) have emerged as a foundational element in the development and applications of quantum algorithms. However, when initialized with random parameter values, PQCs often exhibit barren plateaus (BP). These plateaus, characterized by vanishing gradients with an increasing number of qubits, hinder optimization in quantum algorithms. In this paper, we analyze the impact of state-of-the-art parameter initialization strategies from classical machine learning in random PQCs from the aspect of BP phenomenon. Our investigation encompasses a spectrum of initialization techniques, including random, Xavier (both normal and uniform variants), He, LeCun, and Orthogonal methods. Empirical assessment reveals a pronounced reduction in variance decay of gradients across all these methodologies compared to the randomly initialized PQCs. Specifically, the Xavier initialization technique outperforms the rest, showing a 62% improvement in variance decay compared to the random initialization. The He, Lecun, and orthogonal methods also display improvements, with respective enhancements of 32 %, 28 %, and 26 %. This compellingly suggests that the adoption of these existing initialization techniques holds the potential to significantly amplify the training efficacy of Quantum Neural Networks (QNNs), a subclass of PQCs. Demonstrating this effect, we employ the identified techniques to train QNNs for learning the identity function, effectively mitigating the adverse effects of BPs. The training performance, ranked from the best to the worst, aligns with the variance decay enhancement as outlined above. This paper underscores the role of tailored parameter initialization in mitigating the BP problem and eventually enhancing the training dynamics of QNNs.
Barren plateaus (BPs) pose a major trainability challenge for quantum neural networks (QNNs) by causing gradients to concentrate near zero as circuit size, depth, or expressibility increases. This study presents a comparative benchmark of 10 BP mitigation strategies across six qubit settings (2, 4, 8, 12, 16, and 20) and three datasets of increasing complexity: Iris, MNIST, and MedMNIST. The evaluated methods include eight initialization-based strategies (Beta, Gaussian, Uniform Norm, CNN-based initialization, He-normal, He-uniform, Xavier-normal, and Xavier-uniform), one model-based variational encoder, and one optimization-based time-nonlocal Fourier parameterization. Experiments were implemented using PennyLane 3.10 and PyTorch 2.5 with simulator backends. We evaluate trainability using gradient variance and training loss, and we clarify that the benchmark analyzes simulated QNN optimization behavior rather than hardware-noise-resilient or noisy-label learning. Across the tested two-layer circuit configurations, the mitigation strategies maintained measurable gradient variance and stable loss reduction, suggesting that severe barren plateau behavior was not observed under the benchmark conditions. CNN-based and Beta initialization showed strong empirical behavior in variance retention and convergence speed, while Gaussian initialization was comparatively weaker in higher-dimensional settings. The study provides a reproducible benchmark structure for comparing BP mitigation behavior and identifies important limitations related to circuit depth, hardware noise, feature encoding, and classification performance that should be addressed in future QNN benchmarking.
Variational quantum algorithms (VQAs) have emerged as a leading paradigm in near-term quantum computing, yet their performance can be hindered by the so-called barren plateau problem, where gradients vanish exponentially with system size or circuit depth. While most existing VQA research employs simple Gaussian or zero-initialization schemes, classical deep learning has long benefited from sophisticated weight initialization strategies such as Xavier, He, and orthogonal initialization to improve gradient flow and expedite convergence. In this work, we systematically investigate whether these classical methods can mitigate barren plateaus in quantum circuits. We first review each initialization's theoretical grounding and outline how to adapt the notions from neural networks to VQAs. We then conduct extensive numerical experiments on various circuit architectures and optimization tasks. Our findings indicate that while the initial heuristics, inspired by classical initialization, yield moderate improvements in certain experiments, their overall benefits remain marginal. By outlining a preliminary exploration plan in this paper, we aim to offer the research community a broader perspective and accessible demonstrations. Furthermore, we propose future research directions that may be further refined by leveraging the insights gained from this work.
Barren plateaus, which means the training gradients become extremely small, pose a major challenge in optimizing parameterized quantum circuits, often making the learning process impractically slow or stall. This work shows why using neural networks to generate quantum circuit parameters helps overcome this difficulty. We introduce a geometric viewpoint that describes how the parameters produced by neural networks evolve during training. Our analysis shows that these parameters follow smooth and efficient paths that avoid the flat regions in the training that cause barren plateaus. This provides a computational explanation for the improved trainability observed in recent neural network-assisted quantum learning methods. Overall, our findings bridge ideas from quantum machine learning and computational optimization, offering new insight into the structure of quantum models and guiding future approaches for designing more trainable quantum circuits or parameter initialization.
Abstract In recent years, variational quantum circuits (VQCs) have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic machine-learning models, VQCs can be trained through various optimization approaches, such as gradient-based or gradient-free methods. However, when employing gradient-based methods, the gradient variance of VQCs may dramatically vanish as the number of qubits or layers increases. This issue, a.k.a. barren plateaus (BPs), seriously hinders the scaling of VQCs on large datasets. To mitigate the barren plateaus, extensive efforts have been devoted to tackling this issue through diverse strategies. In this survey, we conduct a systematic literature review of recent works from both investigation and mitigation perspectives. Furthermore, we propose a new taxonomy to categorize most existing mitigation strategies into five groups and introduce them in detail. Also, we compare the concurrent survey papers about BPs. Finally, we provide insightful discussion on future directions for BPs.