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Cited by 480Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Quantum Generative Adversarial Networks for learning and loading random distributions

Open access
Zoufal, Christa, Lucchi, Aurélien, Woerner, Stefan·2019·npj Quantum Information
DOI 10.1038/s41534-019-0223-2
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Abstract

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 $${\mathcal{O}}\left({2}^{n}\right)$$ O 2 n gates to load an exact representation of a generic data structure into an $$n$$ n -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 $${\mathcal{O}}\left(poly\left(n\right)\right)$$ O p o l y n 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.

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  • The product feature map encodes the variable as an N-th degree polynomial formed by {1, x, sqrt(1-x^2)} and their products.

    “Acting on the initial state |Ø this feature map encodes the variable as an N-th degree polynomial formed by {1, x, √ 1x 2 } and their products [73].”

    From Solving nonlinear differential equations with differentiable quantum circuits (2021) · cites this paper as [73]

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Authors
Zoufal, C., Lucchi, A., & Woerner, S.
Affiliations
  • ETH Zurich (CH)
  • IBM Research - Zurich (CH)
Corresponding author
Zoufal, Christa
ORCID
Venue
npj Quantum Information
Publisher
Springer Science and Business Media LLC
Published
2019-11-22
Volume
5
Issue
1
ISSN
2056-6387 (ISSN-L)
DOI
10.1038/s41534-019-0223-2
OpenAlex
W2931020703
Cited by
480
References
28
Citations by year
2026: 84 · 2025: 108 · 2024: 88 · 2023: 72 · 2022: 59 · 2021: 51 · 2020: 17 · 2019: 1
FWCI
14.60
Type
journal article
Language
en
Open access
Licence
Locations
  • npj Quantum Information (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Funders
International Business Machines Corporation
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
quantum generative adversarial networks, probability distribution learning, hybrid quantum-classical algorithms, variational quantum circuits, quantum advantage, quantum amplitude estimation, quantum finance, IBM quantum hardware

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