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arXiv:2205.13418 · Physical Review A

Avoiding barren plateaus with classical deep neural networks

Lucas Friedrich, Jonas Maziero

Published Oct 20, 2022• 49 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.106.042433

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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(\ensuremathθU(\ensuremath{\theta}U(\ensuremathθ) with a classical optimizer that updates the parameters \ensuremathθ\ensuremath{\theta}\ensuremathθ in order to minimize a cost function CCC. 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 \ensuremathθ\ensuremath{\theta}\ensuremathθ used in the parametrization UUU 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.
Abstract Variational quantum algorithms (VQAs) are widely applied in the noisy intermediate-scale quantum era and are expected to demonstrate quantum advantage. However, training VQAs faces difficulties, one of which is the so-called barren plateaus (BPs) phenomenon, where gradients of cost functions vanish exponentially with the number of qubits. In this paper, inspired by transfer learning, where knowledge of pre-solved tasks could be further used in a different but related work with training efficiency improved, we report a parameter initialization method to mitigate BP. In the method, a small-sized task is solved with a VQA. Then the ansatz and its optimum parameters are transferred to tasks with larger sizes. Numerical simulations show that this method could mitigate BP and improve training efficiency. A brief discussion on how this method can work well is also provided. This work provides a reference for mitigating BP, and therefore, VQAs could be applied to more practical problems.
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 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.
Variational quantum algorithms (VQAs) combine the advantages of classical optimization and quantum computation, making them one of the most promising approaches in the Noisy Intermediate-Scale Quantum (NISQ) era. However, when optimized using gradient descent, VQAs often suffer from the vanishing gradient problem, commonly known as the barren plateau. Various methods have been proposed to mitigate this issue. In this work, we propose a hybrid approach that integrates a classical proportional-integral-derivative (PID) controller with a neural network to update the parameters of variational quantum circuits. We refer to this method as NPID, which aims to mitigate the barren plateau. The proposed algorithm is tested on randomly generated quantum input states and random quantum circuits with parametric noise to evaluate its universality, and additional simulations are conducted under different noise rates to examine its robustness. The effectiveness of the proposed method is evaluated based on its convergence speed toward the target cost value. Simulation results show that NPID achieves a convergence efficiency 2-9 times higher than NEQP and QV, with performance fluctuations averaging only 4.45% across different noise levels. These results highlight the potential of integrating classical control theory into quantum optimization, providing a new perspective for improving the trainability and stability of variational quantum algorithms.
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.
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.