Dequantizing quantum machine learning models using tensor networks

• URL: http://arxiv.org/abs/2307.06937v2
• Date: Thu, 21 Dec 2023 14:50:23 GMT
• Title: Dequantizing quantum machine learning models using tensor networks
• Authors: Seongwook Shin, Yong Siah Teo, and Hyunseok Jeong
• Abstract summary: We introduce the dequantizability of the function class of variational quantum-machine-learning(VQML) models. We show that our formalism can properly distinguish VQML models according to their genuine quantum characteristics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ascertaining whether a classical model can efficiently replace a given quantum model -- dequantization -- is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function class of variational quantum-machine-learning~(VQML) models by employing the tensor network formalism, effectively identifying every VQML model as a subclass of matrix product state (MPS) model characterized by constrained coefficient MPS and tensor product-based feature maps. From this formalism, we identify the conditions for which a VQML model's function class is dequantizable or not. Furthermore, we introduce an efficient quantum kernel-induced classical kernel which is as expressive as given any quantum kernel, hinting at a possible way to dequantize quantum kernel methods. This presents a thorough analysis of VQML models and demonstrates the versatility of our tensor-network formalism to properly distinguish VQML models according to their genuine quantum characteristics, thereby unifying classical and quantum machine-learning models within a single framework.

Related papers

• Ground state-based quantum feature maps [17.857341127079305]
  We introduce a quantum data embedding protocol based on the preparation of a ground state of a parameterized Hamiltonian. We show that ground state embeddings can be described effectively by a spectrum with degree that grows rapidly with the number of qubits.
  arXiv  Detail & Related papers  (2024-04-10T17:17:05Z)
• Learning hard distributions with quantum-enhanced Variational Autoencoders [2.545905720487589]
  We introduce a quantum-enhanced VAE (QeVAE) that uses quantum correlations to improve the fidelity over classical VAEs. We empirically show that the QeVAE outperforms classical models on several classes of quantum states. Our work paves the way for new applications of quantum generative learning algorithms.
  arXiv  Detail & Related papers  (2023-05-02T16:50:24Z)
• A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models [62.997667081978825]
  We build over a proposed framework for evaluating the generalization performance of generative models. We establish the first comparative race towards practical quantum advantage (PQA) between classical and quantum generative models. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models.
  arXiv  Detail & Related papers  (2023-03-27T22:48:28Z)
• 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)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Impact of the form of weighted networks on the quantum extreme reservoir computation [0.0]
  The quantum extreme reservoir computation (QERC) is a versatile quantum neural network model. We show how a simple Hamiltonian model based on a disordered discrete time crystal with its simple implementation route provides nearly-optimal performance.
  arXiv  Detail & Related papers  (2022-11-15T01:50:47Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• An Application of Quantum Machine Learning on Quantum Correlated Systems: Quantum Convolutional Neural Network as a Classifier for Many-Body Wavefunctions from the Quantum Variational Eigensolver [0.0]
  Recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits. We present here the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM) The QCNN can be trained to predict the corresponding phase of wavefunctions around the putative quantum critical point, even though it is trained by wavefunctions far away from it.
  arXiv  Detail & Related papers  (2021-11-09T12:08:49Z)
• Structural risk minimization for quantum linear classifiers [0.0]
  Quantum machine learning (QML) stands out as one of the typically highlighted candidates for quantum computing's near-term "killer application" We investigate capacity measures of two closely related QML models called explicit and implicit quantum linear classifiers. We identify that the rank and Frobenius norm of the observables used in the QML model closely control the model's capacity.
  arXiv  Detail & Related papers  (2021-05-12T10:39:55Z)
• Quantum Machine Learning with SQUID [64.53556573827525]
  We present the Scaled QUantum IDentifier (SQUID), an open-source framework for exploring hybrid Quantum-Classical algorithms for classification problems. We provide examples of using SQUID in a standard binary classification problem from the popular MNIST dataset.
  arXiv  Detail & Related papers  (2021-04-30T21:34:11Z)

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.