Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data.However, analytic results to date rely on assumptions and arguments from complexity theory.Because of this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold.Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements.We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes.We use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality.In doing so, we demonstrate that our introduced quantum models are able to outperform state-of-the-art classical models even in practice.
Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data.However, analytic results to date rely on assumptions and arguments from complexity theory.Because of this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold.Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements.We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes.We use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality.In doing so, we demonstrate that our introduced quantum models are able to outperform state-of-the-art classical models even in practice.
Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.
In recent years, classical neural networks have been widely used in various applications and have achieved remarkable success. However, with the advent of quantum computing, there is a growing interest in quantum neural networks (QNNs) as a potential alternative to classical machine learning. In this thesis, we study the architectures of quantum and classical neural networks. We also investigate the performance of QNNs compared to classical neural networks from various aspects, such as vanishing gradient, trainability, expressivity. Our experiments demonstrate that QNNs have the potential to outperform classical neural networks in specific scenarios. While more powerful QNNs exhibit improved performance compared to classical neural networks, our findings also indicate that less powerful QNNs may not always yield significant improvements. This suggests that the effectiveness of QNNs in surpassing classical approaches is contingent on factors such as network architecture, optimization techniques, problem complexity.
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning.Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models.We show theoretically that such quantum-inspired correlations provide a powerful resource for generative modeling.In particular, we provide an unconditional proof of separation in expressive power between a class of widely used generative models, known as Bayesian networks, and its minimal quantum-inspired extension.We show that this expressivity enhancement is associated with quantum nonlocality and quantum contextuality.Furthermore, we numerically test this separation on standard machine-learning data sets and show that it holds for practical problems.The possibility of quantum-inspired enhancement demonstrated in this work not only sheds light on the design of useful quantum machine-learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.
Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the expressivity and inductive bias of QNNs by exploiting an exact mapping from QNNs with inputs x to classical perceptrons acting on x⊗x (generalised to complex inputs). The simplicity of the perceptron architecture allows us to provide clear examples of the shortcomings of current QNN models, and the many barriers they face to becoming useful general-purpose learning algorithms. For example, a QNN with amplitude encoding cannot express the Boolean parity function for n≥3, which is but one of an exponential number of data structures that such a QNN is unable to express. Mapping a QNN to a classical perceptron simplifies training, allowing us to systematically study the inductive biases of other, more expressive embeddings on Boolean data. Several popular embeddings primarily produce an inductive bias towards functions with low class balance, reducing their generalisation performance compared to deep neural network architectures which exhibit much richer inductive biases. We explore two alternate strategies that move beyond standard QNNs. In the first, we use a QNN to help generate a classical DNN-inspired kernel. In the second we draw an analogy to the hierarchical structure of deep neural networks and construct a layered non-linear QNN that is provably fully expressive on Boolean data, while also exhibiting a richer inductive bias than simple QNNs. Finally, we discuss characteristics of the QNN literature that may obscure how hard it is to achieve quantum advantage over deep learning algorithms on classical data.
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 network (QNN) is one of the promising directions where the near-term noisy intermediate-scale quantum (NISQ) devices could find advantageous applications against classical resources. Recurrent neural networks are the most fundamental networks for sequential learning, but up to now there is still a lack of canonical model of quantum recurrent neural network (QRNN), which certainly restricts the research in the field of quantum deep learning. In the present work, we propose a new kind of QRNN which would be a good candidate as the canonical QRNN model, where, the quantum recurrent blocks (QRBs) are constructed in the hardware-efficient way, and the QRNN is built by stacking the QRBs in a staggered way that can greatly reduce the algorithm's requirement with regard to the coherent time of quantum devices. That is, our QRNN is much more accessible on NISQ devices. Furthermore, the performance of the present QRNN model is verified concretely using three different kinds of classical sequential data, i.e., meteorological indicators, stock price, and text categorization. The numerical experiments show that our QRNN achieves much better performance in prediction (classification) accuracy against the classical RNN and state-of-the-art QNN models for sequential learning, and can predict the changing details of temporal sequence data. The practical circuit structure and superior performance indicate that the present QRNN is a promising learning model to find quantum advantageous applications in the near term.