Abstract
We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according to the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits.
Highlights
Quantum computing (QC) has demonstrated superiority in problems intractable on classical computers [1, 2], such as factorization of large numbers [3] and search in an unstructured database [4]
We study the capabilities of the hybrid tensor networks (TN)-variational quantum circuits (VQC) architecture by performing classification tasks on the standard benchmark dataset MNIST [60] and FashionMNIST [61]
We perform the same tasks on a hybrid Principal component analysis (PCA)-VQC model, where the PCA part serves as the simple feature extractor and the VQC as the classifier
Summary
Quantum computing (QC) has demonstrated superiority in problems intractable on classical computers [1, 2], such as factorization of large numbers [3] and search in an unstructured database [4]. For an N -dimensional vector, amplitude encoding requires only log N qubits; the quantum circuit depth to prepare such encoded state exceeds the current limits of NISQ devices. Other approaches like single-qubit rotations require only a shallow circuit but it is unclear how to employ such encoding schemes to load high-dimensional data into a quantum circuit This can be potentially mitigated by preprocessing the input data with classical methods to perform dimension reduction. We propose a hybrid framework where a matrix product state (MPS) [20, 21], the simplest form of tensor networks (TN) [22], is used as a feature extractor to produce a low dimensional feature vector This information is subsequently fed into a VQC for classification.
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