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arXiv:1901.08047 · Quantum Machine Intelligence

Robust implementation of generative modeling with parametrized quantum circuits

Vicente Leyton‐Ortega, Alejandro Perdomo‐Ortiz, Oscar Mario Perdomo

Published May 3, 2021• 37 citations
arXivHTMLPDF
DOI
10.1007/s42484-021-00040-2

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Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum devices, parametrized quantum circuits have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We also demonstrate the ability to evaluate the gradient of the encoded cost function in a quantum state.
In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parametrized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.