Supervised Learning with Tensor Networks

By E. Stoudenmire, David J. Schwab. Neural Information Processing Systems, 2016

490 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/88332ba4348a5c5fc5a97ceeeff19ba937611d2d

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Citations in the corpus

Variational quantum algorithms (2020, background): “Interestingly, the tensor network structure of quantum mechanics has even inspired classical machine learning methods [136].”
Long-term Forecasting using Tensor-Train RNNs (2017, background): “(Stoudenmire & Schwab, 2016) propose to parameterizes the supervised learning models with matrix-product states for image classiﬁcation.”
Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification (2021, unknown): “Recently, there are an increasing number of emerging tensor network applications in machine learning [3][4].”
Efficient non-Markovian quantum dynamics using time-evolving matrix product operators (2017, background): “Moreover there has been a recent synthesis showing how techniques developed in one context can be extended to others, such as machine learning [50], or Monte Carlo sampling of quantum states [51].”
Circuit-centric quantum classifiers (2018, background): “and can give rise to interesting nonlinearities that may facilitate the classification procedure in the following steps (see also [28]).”
Supervised learning with quantum-enhanced feature spaces (2018, methodology): “…space of Euler angles for the individual qubits, so that the full feature map can be implemented as: Φ : One example for such an implementation is the unitary implementation of the feature map used in the context of the classical classiﬁers by Stoudenmire and Schwab [31] based on tensor networks.”
Parameterized quantum circuits as machine learning models (2019, background): “[15] Edwin Stoudenmire and David J Schwab, “Supervised learning with tensor networks,” in Advances in Neural Information Processing Systems 29 , edited by D.”
A generative modeling approach for benchmarking and training shallow quantum circuits (2018, background): “Previous implementations of Born machines [25–28] often relied on the construction of tensor networks and their efficient manipulation through graphical-processing units.”
Robust data encodings for quantum classifiers (2020, methodology): “[65] E.”
Towards quantum machine learning with tensor networks (2018, background): “With classical resources, tensor network models already give very good results for supervised [12, 13, 15, 17] and unsupervised [17, 19] learning tasks.”
Long-term Forecasting using Higher Order Tensor RNNs (2017, methodology): “es all these works to capture higher-order interactions using a hidden-to-hidden tensor. Tensor methods Tensor methods have tight connections with neural networks. For example, (Novikov et al., 2015; Stoudenmire and Schwab, 2016) employ tensor-train to compress the weights in neural networks. (Yang ”
The ITensor Software Library for Tensor Network Calculations (2020, methodology): “arning is an area where ITensor has potential to be used much more in the future, and ITensor has already been used to investigate new models and algorithms for machine learning, including supervised [50,51] and unsupervised [52] learning using models parameterized by tensor networks, and to investi”
Hierarchical quantum classifiers (2018, methodology): “ increasing the input and internal bond dimensions. This is equivalent to performing computation using qudits. Data can be encoded in qudits using a generalization of qubit encoding described in Ref. [29]. Whilst it is possible to simulate qudits with qubits, there are practical considerations that ”