NRQNN: The Role of Observable Selection in Noise-Resilient Quantum Neural Networks

Abstract: This paper explores the complexities associated with training Quantum Neural Networks (QNNs) under noisy conditions, a critical consideration for Noisy Intermediate-Scale Quantum (NISQ) devices. We first demonstrate that Barren Plateaus (BPs), characterized by exponetially vanishing gradients, emerge more readily in noisy quantum environments than in ideal conditions. We then propose that careful selection of qubit measurement observable can make QNNs resilient against noise. To this end, we explore the effectiveness of various qubit measurement observables, including PauliX, PauliY, PauliZ, and a custom designed Hermitian observable, against three types of quantum noise: Phase Damping, Phase Flip, and Amplitude Damping. Our findings reveal that QNNs employing Pauli observables are prone to an earlier emergence of BPs, notably in noisy environments, even with a smaller qubit count of four qubits. Conversely, the custom designed Hermitian measurement observable exhibits significant resilience against all types of quantum noise, facilitating consistent trainability for QNNs up to 10 qubits. This study highlights the crucial role of observable selection and quantum noise consideration in enhancing QNN training, offering a strategic approach to improve QNN performance in NISQ era.