Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

• URL: http://arxiv.org/abs/2104.02249v1
• Date: Tue, 6 Apr 2021 02:31:48 GMT
• Title: Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• Authors: Michael L. Wall, Giuseppe D'Aguanno
• Abstract summary: We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. We present an approach that can be implemented on gate-based quantum computing devices.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree tensor network (TTN) topology, which acts as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion. This unsupervised feature extractor then feeds a supervised linear classifier and encodes the output in a small-dimensional quantum register. In contrast to previous work on \emph{quantum-inspired} TTN classifiers, in which the embedding map and class decision weights did not map the data to well-defined quantum states, we present an approach that can be implemented on gate-based quantum computing devices. In particular, we identify an embedding map with accuracy similar to exponential machines (Novikov \emph{et al.}, arXiv:1605.03795), but which produces valid quantum states from classical data vectors, and utilize manifold-based gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one- and two-point correlation functions of the decision boundary vectors of the quantum model, which can be used for model interpretability, as well as methods for obtaining classifications from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights, and may produce models that are less susceptible to adversarial perturbations. We demonstrate our methodologies in applications utilizing the MNIST handwritten digit dataset and a multivariate timeseries dataset of human activity recognition.

Related papers

• MORE: Measurement and Correlation Based Variational Quantum Circuit for Multi-classification [10.969833959443495]
  MORE stands for measurement and correlation based variational quantum multi-classifier. We implement MORE using the Qiskit Python library and evaluate it through extensive experiments on both noise-free and noisy quantum systems.
  arXiv  Detail & Related papers  (2023-07-21T19:33:10Z)
• 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)
• 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)
• Quantum variational learning for entanglement witnessing [0.0]
  This work focuses on the potential implementation of quantum algorithms allowing to properly classify quantum states defined over a single register of $n$ qubits. We exploit the notion of "entanglement witness", i.e., an operator whose expectation values allow to identify certain specific states as entangled. We made use of Quantum Neural Networks (QNNs) in order to successfully learn how to reproduce the action of an entanglement witness.
  arXiv  Detail & Related papers  (2022-05-20T20:14:28Z)
• Noisy Quantum Kernel Machines [58.09028887465797]
  An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. We study how dissipation and decoherence affect their performance. We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
  arXiv  Detail & Related papers  (2022-04-26T09:52:02Z)
• A tensor network discriminator architecture for classification of quantum data on quantum computers [0.0]
  We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms. We experimentally evaluate models on Quantinuum's H1-2 trapped ion quantum computer using entangled input data modeled as translationally invariant, bond 4 MPSs.
  arXiv  Detail & Related papers  (2022-02-22T14:19:42Z)
• Scalable approach to many-body localization via quantum data [69.3939291118954]
  Many-body localization is a notoriously difficult phenomenon from quantum many-body physics. We propose a flexible neural network based learning approach that circumvents any computationally expensive step. Our approach can be applied to large-scale quantum experiments to provide new insights into quantum many-body physics.
  arXiv  Detail & Related papers  (2022-02-17T19:00:09Z)
• Quantum-tailored machine-learning characterization of a superconducting qubit [50.591267188664666]
  We develop an approach to characterize the dynamics of a quantum device and learn device parameters. This approach outperforms physics-agnostic recurrent neural networks trained on numerically generated and experimental data. This demonstration shows how leveraging domain knowledge improves the accuracy and efficiency of this characterization task.
  arXiv  Detail & Related papers  (2021-06-24T15:58:57Z)
• Facial Expression Recognition on a Quantum Computer [68.8204255655161]
  We show a possible solution to facial expression recognition using a quantum machine learning approach. We define a quantum circuit that manipulates the graphs adjacency matrices encoded into the amplitudes of some appropriately defined quantum states.
  arXiv  Detail & Related papers  (2021-02-09T13:48:00Z)
• Quantum embeddings for machine learning [5.16230883032882]
  Quantum classifiers are trainable quantum circuits used as machine learning models. We propose to train the first part of the circuit -- the embedding -- with the objective of maximally separating data classes in Hilbert space. This approach provides a powerful analytic framework for quantum machine learning.
  arXiv  Detail & Related papers  (2020-01-10T19:00:01Z)

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.