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Quantum Information Processing

Impact of barren plateaus countermeasures on the quantum neural network capacity to learn

Jacob L. Cybulski, Thanh Thi Nguyen

Published Dec 14, 2023• 10 citations
Publisher
DOI
10.1007/s11128-023-04187-8

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Barren plateaus -- the exponential vanishing of gradients -- are a fundamental obstacle to training scalable quantum neural networks. Whether they arise in quantum recurrent neural networks (QRNNs), a natural architecture for sequential data, remains a pressing question. Here we show that the decisive ingredient for trainability in QRNNs is not the recurrent circuit topology per se, but enforcing time-translation symmetry through parameter sharing across time steps. We prove that, without parameter sharing, QRNNs suffer from barren plateaus, with gradient variance decaying exponentially with sequence length. Imposing parameter sharing across time steps fundamentally alters this scaling, transforming it into a polynomial dependence and thereby suppressing the barren plateau. Numerical simulations corroborate these analytical predictions. By rigorously showing how time-translation symmetry suppresses barren plateaus and enhances learning capability in QRNNs, our work establishes task-aligned symmetry as a constructive resolution to the expressivity-trainability tension in quantum neural networks.
Effective training of Quantum Neural Networks (QNNs) is crucial in the Noisy Intermediate-Scale Quantum (NISQ) era, where noise accelerates the onset of barren plateaus (BPs) and limits scalability. This paper investigates how quantum noise impacts QNN trainability and demonstrates that careful selection of qubit measurement observables can mitigate these effects. We analyze PauliX, PauliY, PauliZ, and a customized Hermitian observable under both global (all-qubit measured) and local (single-qubit measured) cost functions. Our results show that with global cost function, PauliX and PauliY lead to flatter landscapes under noise, while PauliZ maintains training up to 8 qubits before encountering BPs. The customized Hermitian observable proves most robust, enabling training up to 10 qubits in noisy settings. For local cost function setting, PauliZ outperforms PauliX and PauliY, maintaining efficiency up to 10 qubits. These findings highlight the importance of noise-aware observable selection, offering a practical strategy to improve QNN performance and advance quantum machine learning in noisy environments.