The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bounds than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that quantum neural networks (QNNs) have the ability to achieve this goal on specific datasets. In this regard, it is of great importance to understand whether these advantages are still preserved on real-world tasks. Through systematic numerical experiments, we empirically observe that current QNNs fail to provide any benefit over classical learning models. Concretely, our results deliver two key messages. First, QNNs suffer from the severely limited effective model capacity, which incurs poor generalization on real-world datasets. Second, the trainability of QNNs is insensitive to regularization techniques, which sharply contrasts with the classical scenario. These empirical results force us to rethink the role of current QNNs and to design novel protocols for solving real-world problems with quantum advantages.
The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bounds than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that quantum neural networks (QNNs) have the ability to achieve this goal on specific datasets. In this regard, it is of great importance to understand whether these advantages are still preserved on real-world tasks. Through systematic numerical experiments, we empirically observe that current QNNs fail to provide any benefit over classical learning models. Concretely, our results deliver two key messages. First, QNNs suffer from the severely limited effective model capacity, which incurs poor generalization on real-world datasets. Second, the trainability of QNNs is insensitive to regularization techniques, which sharply contrasts with the classical scenario. These empirical results force us to rethink the role of current QNNs and to design novel protocols for solving real-world problems with quantum advantages.
The development of quantum neural networks (QNNs) has attracted considerable attention due to their potential to surpass classical models in certain machine learning tasks. Nonetheless, it remains unclear under which conditions QNNs provide concrete benefits over classical neural networks (CNNs). This study addresses this question by performing both qualitative and quantitative analyses of classical and quantum models applied to regression problems, using two target functions with contrasting properties. Additionally, the work explores the methodological difficulties inherent in making fair comparisons between QNNs and CNNs. The findings reveal a distinct advantage of QNNs in a specific quantum machine learning context. In particular, QNNs excelled at approximating the sinusoidal function, achieving errors up to seven orders of magnitude lower than their classical counterparts. However, their performance was limited in other cases, emphasizing that QNNs are highly effective for certain tasks but not universally superior. These results reinforce the principles of the “No Free Lunch” theorem, highlighting that no single model outperforms all others across every problem domain.
The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.
The development of quantum neural networks (QNNs) has attracted considerable attention due to their potential to surpass classical models in certain machine learning tasks. Nonetheless, it remains unclear under which conditions QNNs provide concrete benefits over classical neural networks (CNNs). This study addresses this question by performing both qualitative and quantitative analyses of classical and quantum models applied to regression problems, using two target functions with contrasting properties. Additionally, the work explores the methodological difficulties inherent in making fair comparisons between QNNs and CNNs. The findings reveal a distinct advantage of QNNs in a specific quantum machine learning context. In particular, QNNs excelled at approximating the sinusoidal function, achieving errors up to seven orders of magnitude lower than their classical counterparts. However, their performance was limited in other cases, emphasizing that QNNs are highly effective for certain tasks but not universally sPuperior. These results reinforce the principles of the ``No Free Lunch'' theorem, highlighting that no single model outperforms all others across every problem domain.
Quantum machine learning (QML) is an emerging research area that combines quantum computation with classical machine learning (ML). The primary objective of QML is to enhance the performance of traditional ML algorithms by harnessing quantum phenomena. Inspired by the success of classical neural networks (NNs), their quantum analog, commonly known as quantum neural networks (QNNs), are widely being investigated. Despite the significant interest, the literature still lacks some concrete evidence about QNN's superiority over their classical counterparts, especially in practical applications. This paper empirically demonstrates a greater capacity in hybrid quantum neural networks (HQNNs) for a practical application, namely multi-class classification. In particular, we train both the HQNNs and their equivalent classical counterparts on the same data. We then benchmark the models' accuracy for quantifying model's capacity, where greater accuracy typically implies greater capacity. The results demonstrate a clear quantum advantage, i.e., greater capacity of HQNNs over their classical counterparts, where the HQNN models constantly achieve better accuracy. This superiority in performance by HQNNs serves as a foundational study for further investigation to magnify the quantum advantage in real-world applications of HQNNs.
Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their generalization properties, are less developed and primarily focus on the uniform convergence approach. In this paper, we exploit an advanced tool in classical learning theory, i.e., algorithmic stability, to study the generalization of QNNs. We first establish high-probability generalization bounds for QNNs via uniform stability. Our bounds shed light on the key factors influencing the generalization performance of QNNs and provide practical insights into both the design and training processes. We next explore the generalization of QNNs on near-term noisy intermediate-scale quantum (NISQ) devices, highlighting the potential benefits of quantum noise. Moreover, we argue that our previous analysis characterizes worst-case generalization guarantees, and we establish a refined optimization-dependent generalization bound for QNNs via on-average stability. Numerical experiments on various real-world datasets support our theoretical findings.
Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the study of quantum models for machine learning tasks.