Quantum Generative Adversarial Networks for learning and loading random distributions

By Christa Zoufal, Aurélien Lucchi, Stefan Woerner. npj Quantum Information, 2019

616 citations recorded by the source corpus.

Quantum algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best known methods require O2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{O}}\left({2}^{n}\right)$$\end{document} gates to load an exact representation of a generic data structure into an n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-qubit state. This scaling can easily predominate the complexity of a quantum algorithm and, thereby, impair potential quantum advantage. Our work presents a hybrid quantum-classical algorithm for efficient, approximate quantum state loading. More precisely, we use quantum Generative Adversarial Networks (qGANs) to facilitate efficient learning and loading of generic probability distributions - implicitly given by data samples - into quantum states. Through the interplay of a quantum channel, such as a variational quantum circuit, and a classical neural network, the qGAN can learn a representation of the probability distribution underlying the data samples and load it into a quantum state. The loading requires Opolyn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{O}}\left(poly\left(n\right)\right)$$\end{document} gates and can thus enable the use of potentially advantageous quantum algorithms, such as Quantum Amplitude Estimation. We implement the qGAN distribution learning and loading method with Qiskit and test it using a quantum simulation as well as actual quantum processors provided by the IBM Q Experience. Furthermore, we employ quantum simulation to demonstrate the use of the trained quantum channel in a quantum finance application.

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

View Paper: https://www.semanticscholar.org/paper/b1a472bc988e28d4910c91fa4dd1077d545a5239

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Stefan Woerner

Citations in the corpus

Parameterized quantum circuits as machine learning models (2019, background): “Zoufal et al. [76] propose a QGAN to approximately perform amplitude encoding.”
Option Pricing using Quantum Computers (2019, methodology): “These networks allow us to load a distribution using a polynomial number of gates [19].”
Quantum Computing for Finance: State-of-the-Art and Future Prospects (2020, background): “This enables approximate data loading schemes, which have some potential to work around this problem [57].”
The power of quantum neural networks (2020, methodology): “Some proposals for quantum neural networks include [4–11] and hint at potential advantages, such as speed-ups in training and faster processing.”