Enhancing Variational Quantum Circuit Training: An Improved Neural Network Approach for Barren Plateau Mitigation

TL;DR

This work tackles barren plateaus in variational quantum circuits by refining a neural-network–based BP mitigation strategy and broadening its applicability to Haar-random quantum inputs and randomized circuit structures, resulting in the Neural Enhanced Quantum Circuit (NEQC). The method trains a neural network to map inputs to VQC parameters, enabling SQC-NN and two NEQC architectures (NEQC-NN and NEQC-CNN) that demonstrate faster convergence and smoother loss landscapes compared to standard VQCs. Expressibility analyses show NEQC variants become less expressible, which correlates with improved trainability and BP mitigation. The approach exhibits universal applicability to VQAs for quantum state preparation and beyond, potentially benefiting QAOA, VQE, and quantum architecture search in diverse domains, with a parameter count of $3N+4L$ for a circuit with $N$ qubits and $L$ blocks.

Abstract

Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. Similar to neural networks (NNs), VQAs iteratively update circuit parameters to optimize a cost function. However, the training of variational quantum circuits (VQCs) is susceptible to a phenomenon known as barren plateaus (BPs). Various methods 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 this approach by comparing the convergence speed before and after it is utilized. Furthermore, we give an explanation for the effectiveness of this method 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 method'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.

Figures (4)

• Figure 1: The construction of quantum circuits with random structures
• Figure 2: Illustration of the SQC and NEQC models. (a) The circuit parameters in the Standard Quantum Circuit (SQC) are directly initialized and iteratively updated. (b) The circuit parameters in the Neural Enhanced Quantum Circuit (NEQC) are derived from the neural network. The input vector and the parameters of the neural network are iteratively updated.
• Figure 3: The variation of average loss with respect to the number of iterations.
• Figure 4: Loss landscapes for various qubits counts and models. The left, middle, and right columns correspond to the SQC, NEQC-NN, and NEQC-CNN models, respectively. The rows, from top to bottom, correspond to 3 to 8 qubits.