Related papers: Expressibility-induced Concentration of Quantum Ne…
Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model…
Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We…
Fault-tolerant quantum computers offer the promise of dramatically improving machine learning through speed-ups in computation or improved model scalability. In the near-term, however, the benefits of quantum machine learning are not so…
Quantum variational algorithms have been one of major applications of quantum computing with current quantum devices. There are recent attempts to establish the foundation for these algorithms. A possible approach is to characterize the…
Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear.…
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…
Quantum kernel method is one of the key approaches to quantum machine learning, which has the advantages that it does not require optimization and has theoretical simplicity. By virtue of these properties, several experimental…
Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of…
One of the most natural connections between quantum and classical machine learning has been established in the context of kernel methods. Kernel methods rely on kernels, which are inner products of feature vectors living in large feature…
Yang (2020a) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their analysis does not…
We analyze the expressivity of a universal deep neural network that can be organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads. While the maximal expressive power increases with the depth of the…
Knowing whether a Quantum Machine Learning model would perform well on a given dataset before training it can help to save critical resources. However, gathering a priori information about model performance (e.g., training speed, critical…
Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…
Machine learning is widely believed to be one of the most promising practical applications of quantum computing. Existing quantum machine learning schemes typically employ a quantum-classical hybrid approach that relies crucially on…
Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems. Identifying hyperparameters controlling the inductive bias of quantum machine learning models is expected to be crucial…
Quantum computers are known to provide speedups over classical state-of-the-art machine learning methods in some specialized settings. For example, quantum kernel methods have been shown to provide an exponential speedup on a learning…
Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks. In the infinite-width limit, NTKs can easily be computed for most common architectures, yielding full analytic control over the training…
Quantum generative models provide inherently efficient sampling strategies and thus show promise for achieving an advantage using quantum hardware. In this work, we investigate the barriers to the trainability of quantum generative models…
Hybrid quantum neural networks (HQNNs) integrate parameterized quantum circuits (PQCs) within classical networks, where the behavior of the underlying PQCs is often the primary focus of analysis. In this context, expressibility and…
Recent theoretical works based on the neural tangent kernel (NTK) have shed light on the optimization and generalization of over-parameterized networks, and partially bridge the gap between their practical success and classical learning…