HQNET: Harnessing Quantum Noise for Effective Training of Quantum Neural Networks in NISQ Era

This paper delves into the intricate dynamics of quantum noise and its influence on the onset and mitigation of barren plateaus (BPs) - a phenomenon that critically impedes the scalability of QNNs. We find that BPs appear earlier in noisy quantum environments compared to ideal, noise-free conditions.However, strategic selection of qubit measurement observables can effectively tackle this issue. To this end, we examine a variety of observables, such as PauliZ,PauliX, PauliY, and a specially designed arbitrary Hermitian observable, tailored to the requirements of the cost function and the desired outputs of quantum circuits. Our analysis encompasses both global and local cost function definitions, with the former involving measurements across all qubits and the latter focusing on single-qubit measurements within the QNN framework. Our findings indicate that in a global cost function scenario, PauliX and PauliY observables lead to flatter optimization landscapes, signaling BPs with increasing qubits, especially in noisy conditions. Conversely, the PauliZ observable maintains trainability up to 8 qubits but encounters BPs at 10 qubits. Notably, the arbitrary Hermitian observable, when used with a global cost function, shows a unique advantage as it benefits from noise, facilitating effective training up to 10 qubits. Furthermore, with a local cost function, out of the three conventional observables (PauliX, PauliY and PauliZ), PauliZ is more effective, sustaining training efficiency under noisy conditions for up to 10 qubits, while PauliX and PauliY do not show similar benefits and remain susceptible to BPs. Our results highlight the importance of noise consideration in QNN training and propose a strategic approach to observable selection to improve QNN performance in noisy quantum computing environments thus contributing to the advancement of quantum machine learning research.