Towards quantum machine learning with tensor networks

By William J. Huggins, P. Patil, B. Mitchell, K. Birgitta Whaley, E. Stoudenmire. Quantum Science and Technology, 2018

410 citations recorded by the source corpus.

Machine learning is a promising application of quantum computing, but challenges remain for implementation today because near-term devices have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks, that could already have benefits with such near-term devices. The result is a unified framework in which classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes in which, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a hybrid quantum-classical optimization procedure that could be carried out on quantum hardware today, and testing the noise resilience of the trained model.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5a4a50f6155e8cb7ee95772194f696a4a1aff0b4

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, methodology): “Tensor networks are also being widely used in machine learning (Carleo et al., 2019; Glasser et al., 2018, 2019; Huggins et al., 2019; Stoudenmire and Schwab, 2016).”
Hierarchical quantum classifiers (2018, methodology): “Moreover, a hybrid approach that involves a classical pre-training step to initialize some of the gates has been previously proposed.(16) We empirically validate this approach by initializing a 1D MERA with a pre-trained 1D TTN.”
Parameterized quantum circuits as machine learning models (2019, methodology): “Huggins et al. [29] suggest a qubit-eﬃcient version where the traced qubits are reinitialized and used as the inputs of another unitary, as shown in Fig.”
PennyLane: Automatic differentiation of hybrid quantum-classical computations (2018, background): “Different types of architectures for variational circuits: (I) layered gate architecture, (II) alternating operator architecture [ 2 ] , and (III) an example of a tensor network architecture [ 39 ] .”
Quantum Natural Gradient (2019, methodology): “Applications include the Variational Quantum Eigensolver (VQE) [20], Quantum Approximate Optimization Algorithm (QAOA) [5] and Quantum Neural Networks (QNNs) [6, 10, 23].”
Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future (2019, background): “A tensor network inspired QC approach to both discriminative and generative learning models has been proposed in [177], where the near-future quantum devices with a limited number of physical qubits and high error-rate are targeted.”
Quantum technology for military applications (2021, background): “Such applicability can be accelerated by hybrid classical-quantum machine learning where tensor network models could be implemented on small near-term quantum devices [185].”
Unsupervised Generative Modeling Using Matrix Product States (2017, background): “[67] William Huggins, Piyush Patel, K Birgitta Whaley, and E Miles Stoudenmire, “Towards quantum machine learning with tensor networks,” arXiv preprint arXiv:1803.”