Arbitrary Polynomial Separations in Trainable Quantum Machine Learning

• URL: http://arxiv.org/abs/2402.08606v1
• Date: Tue, 13 Feb 2024 17:12:01 GMT
• Title: Arbitrary Polynomial Separations in Trainable Quantum Machine Learning
• Authors: Eric R. Anschuetz and Xun Gao
• Abstract summary: 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. We here circumvent these negative results by constructing a hierarchy of efficiently train QNNs that exhibit unconditionally provable, memory separations. We show that quantum contextuality is the source of the expressivity separation, suggesting that other classical sequence learning problems with long-time correlations may be a regime where practical advantages in quantum machine learning may exist.
• Score: 1.0080317855851213
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 in performing a classical sequence modeling task. Furthermore, each unit cell of the introduced class of QNNs is computationally efficient, implementable in constant time on a quantum device. The classical networks we prove a separation over include well-known examples such as recurrent neural networks and Transformers. We show that quantum contextuality is the source of the expressivity separation, suggesting that other classical sequence learning problems with long-time correlations may be a regime where practical advantages in quantum machine learning may exist.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Information-driven Nonlinear Quantum Neuron [0.0]
  In this study, a hardware-efficient quantum neural network operating as an open quantum system is proposed. We show that this dissipative model based on repeated interactions, which allows for easy parametrization of input quantum information, exhibits differentiable, non-linear activation functions.
  arXiv  Detail & Related papers  (2023-07-18T07:12:08Z)
• Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification [83.20479832949069]
  Quantum neural networks (QNNs) have become an important tool for understanding the physical world, but their advantages and limitations are not fully understood. Here we investigate the problem-dependent power of QCs on multi-class classification tasks. Our work sheds light on the problem-dependent power of QNNs and offers a practical tool for evaluating their potential merit.
  arXiv  Detail & Related papers  (2022-12-29T10:46:40Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• A didactic approach to quantum machine learning with a single qubit [68.8204255655161]
  We focus on the case of learning with a single qubit, using data re-uploading techniques. We implement the different proposed formulations in toy and real-world datasets using the qiskit quantum computing SDK.
  arXiv  Detail & Related papers  (2022-11-23T18:25:32Z)
• Efficient and quantum-adaptive machine learning with fermion neural networks [8.537841858846082]
  We propose fermion neural networks (FNNs) whose physical properties serve as outputs, once the inputs are incorporated as an initial layer. We establish an efficient optimization, which entitles FNNs to competitive performance on challenging machine-learning benchmarks.
  arXiv  Detail & Related papers  (2022-11-10T19:00:02Z)
• Interpretable Quantum Advantage in Neural Sequence Learning [2.575030923243061]
  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 pinpoint quantum contextuality as the source of an unconditional memory separation in the expressivity of the two model classes. In doing so, we demonstrate that our introduced quantum models are able to outperform state of the art classical models even in practice.
  arXiv  Detail & Related papers  (2022-09-28T18:34:04Z)
• Power and limitations of single-qubit native quantum neural networks [5.526775342940154]
  Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. We formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks.
  arXiv  Detail & Related papers  (2022-05-16T17:58:27Z)
• The dilemma of quantum neural networks [63.82713636522488]
  We show that quantum neural networks (QNNs) fail to provide any benefit over classical learning models. QNNs suffer from the severely limited effective model capacity, which incurs poor generalization on real-world datasets. These results force us to rethink the role of current QNNs and to design novel protocols for solving real-world problems with quantum advantages.
  arXiv  Detail & Related papers  (2021-06-09T10:41:47Z)
• Mutual Reinforcement between Neural Networks and Quantum Physics [0.0]
  Quantum machine learning emerges from the symbiosis of quantum mechanics and machine learning. The use of classical machine learning as a tool applied to quantum physics problems. The design of a quantum neural network based on the dynamics of a quantum perceptron with the application of shortcuts to adiabaticity gives rise to a short operation time and robust performance.
  arXiv  Detail & Related papers  (2021-05-27T16:20:50Z)
• Entanglement Classification via Neural Network Quantum States [58.720142291102135]
  In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS)
  arXiv  Detail & Related papers  (2019-12-31T07:40:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.