Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Survey

TL;DR

The paper addresses the challenge of barren plateaus (BPs) in variational quantum circuits (VQCs), where gradient variance vanishes as system size grows, hindering scalable training. It proposes a two-part taxonomy separating investigation and mitigation, and surveys a broad range of strategies across initialization, optimization, model architecture, regularization, and measurement to combat BPs. The work synthesizes findings from numerous studies, contrasts them with concurrent surveys, and discusses future directions such as AI-driven initialization and novel circuit designs. Overall, the survey provides a structured framework and practical insights to improve the trainability of VQCs in the NISQ era, with implications for quantum chemistry, quantum machine learning, and related applications.

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.

Figures (6)

• Figure 1: Our proposed taxonomy. We categorize the most existing works about barren plateaus into two aspects: investigation and mitigation.
• Figure 2: A general structure of a VQC where the initialization-based strategy is circled in a dotted box. Generally speaking, a VQC will take the encoded quantum-state data as inputs and learn the data representation through a sequence of unitary operations. For each unitary gate, VQC has a corresponding parameter. In the beginning, initialization-based strategies $V(\theta)$ are applied to initialize parameters $\theta$ of the unitary quantum circuits $U(\theta)$ before training. In the end, a measurement layer is applied to measure the output of the VQC.
• Figure 3: A general structure of VQCs where the optimization-based strategies are usually applied in the training of $U(\theta)$ (dotted box), which is decomposed into $L$ layer from $U_1(\theta_1)$ to $U_L(\theta_L)$ (upper side). On the lower side, we present the process for addressing BPs. The left-most cost-function landscape represents BPs, a flat landscape with no discernible slope towards the minimum. In this case, many optimization approaches may be initially trapped in the flat landscape, leading to a failure of training. By employing optimization-based strategies, the cost-function landscape could be gradually recovered, as shown in the middle and right-most landscapes.
• Figure 4: An overall idea of model-based strategies that are usually applied to the decomposed unitary circuit $U(\theta) \in \mathbf{C}^{n\cdot L}$ (dotted box), where $U_L^n$ denotes that $U(\theta)$ consists of $n$ qubits and $L$ layers.
• Figure 5: An overall idea of regularization-based strategies. This strategy could be applied to the model parameters during initialization or training. We use dotted circles to represent the regularization in this figure.