Enhancing the expressivity of quantum neural networks with residual connections

• URL: http://arxiv.org/abs/2401.15871v1
• Date: Mon, 29 Jan 2024 04:00:51 GMT
• Title: Enhancing the expressivity of quantum neural networks with residual connections
• Authors: Jingwei Wen, Zhiguo Huang, Dunbo Cai, Ling Qian
• Abstract summary: We propose a quantum circuit-based algorithm to implement quantum residual neural networks (QResNets) Our work lays the foundation for a complete quantum implementation of the classical residual neural networks.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the recent noisy intermediate-scale quantum era, the research on the combination of artificial intelligence and quantum computing has been greatly developed. Inspired by neural networks, developing quantum neural networks with specific structures is one of the most promising directions for improving network performance. In this work, we propose a quantum circuit-based algorithm to implement quantum residual neural networks (QResNets), where the residual connection channels are constructed by introducing auxiliary qubits to the data-encoding and trainable blocks of the quantum neural networks. Importantly, we prove that when this particular network architecture is applied to a $l$-layer data-encoding, the number of frequency generation forms can be extended from one, namely the difference of the sum of generator eigenvalues, to $\mathcal{O}(l^2)$. And the flexibility in adjusting the corresponding Fourier coefficients can also be improved due to the diversity of spectrum construction methods and the additional optimization degrees of freedom in the generalized residual operators. These results indicate that the residual encoding scheme can achieve better spectral richness and enhance the expressivity of various parameterized quantum circuits. Extensive numerical demonstrations in regression tasks of fitting various functions and applications in image classification with MNIST datasets are offered to present the expressivity enhancement. Our work lays the foundation for a complete quantum implementation of the classical residual neural networks and explores a new strategy for quantum feature map in quantum machine learning.

Related papers

• Distributed Quantum Neural Networks via Partitioned Features Encoding [0.0]
  Quantum neural networks are expected to be a promising application in near-term quantum computing. We propose to make a prediction by approximating outputs of a large circuit using multiple small circuits. Our proposed method not only achieved highly accurate predictions for a large dataset but also reduced the hardware requirements for each quantum neural network.
  arXiv  Detail & Related papers  (2023-12-21T08:21:44Z)
• Realization of a quantum neural network using repeat-until-success circuits in a superconducting quantum processor [0.0]
  In this paper, we use repeat-until-success circuits enabled by real-time control-flow feedback to realize quantum neurons with non-linear activation functions. As an example, we construct a minimal feedforward quantum neural network capable of learning all 2-to-1-bit Boolean functions. This model is shown to perform non-linear classification and effectively learns from multiple copies of a single training state consisting of the maximal superposition of all inputs.
  arXiv  Detail & Related papers  (2022-12-21T03:26:32Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• 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)
• A quantum algorithm for training wide and deep classical neural networks [72.2614468437919]
  We show that conditions amenable to classical trainability via gradient descent coincide with those necessary for efficiently solving quantum linear systems. We numerically demonstrate that the MNIST image dataset satisfies such conditions. We provide empirical evidence for $O(log n)$ training of a convolutional neural network with pooling.
  arXiv  Detail & Related papers  (2021-07-19T23:41:03Z)
• Entanglement Rate Optimization in Heterogeneous Quantum Communication Networks [79.8886946157912]
  Quantum communication networks are emerging as a promising technology that could constitute a key building block in future communication networks in the 6G era and beyond. Recent advances led to the deployment of small- and large-scale quantum communication networks with real quantum hardware. In quantum networks, entanglement is a key resource that allows for data transmission between different nodes.
  arXiv  Detail & Related papers  (2021-05-30T11:34:23Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• Variational learning for quantum artificial neural networks [0.0]
  We first review a series of recent works describing the implementation of artificial neurons and feed-forward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. While keeping full compatibility with the overall memory-efficient feed-forward architecture, our constructions effectively reduce the quantum circuit depth required to determine the activation probability of single neurons.
  arXiv  Detail & Related papers  (2021-03-03T16:10:15Z)
• Recurrent Quantum Neural Networks [7.6146285961466]
  Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning. We construct a quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks. We evaluate the QRNN on MNIST classification, both by feeding the QRNN each image pixel-by-pixel; and by utilising modern data augmentation as preprocessing step.
  arXiv  Detail & Related papers  (2020-06-25T17:59:44Z)
• 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.