Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1901.00848 · Advanced Quantum Technologies

Variational Quantum Generators: Generative Adversarial Quantum Machine Learning for Continuous Distributions

Jonathan Romero, Alán Aspuru‐Guzik

Published Dec 3, 2020• 185 citations
arXivHTMLPDF

Abstract

Abstract A hybrid quantum–classical approach to model continuous classical probability distributions using a variational quantum circuit is proposed. The architecture of this quantum generator consists of a quantum circuit that encodes a classical random variable into a quantum state and a parameterized quantum circuit trained to mimic the target distribution. The model allows for easy interfacing with a classical function, such as a neural network, and is trained using an adversarial learning approach. It is shown that the quantum generator is able to learn using either a classical neural network or a variational quantum circuit as the discriminator model. This implementation takes advantage of automatic differentiation tools to perform the optimization of the variational circuits employed. The framework presented here for the design and implementation of the variational quantum generators can serve as a blueprint for designing hybrid quantum–classical models for other machine learning tasks.

DOI
10.1002/qute.202000003

Related papers

Variational Quantum Circuits Enhanced Generative Adversarial Network

Runqiu Shu, Xusheng Xu, Man‐Hong Yung +1 more

Generative adversarial network (GAN) is one of the widely-adopted machine-learning frameworks for a wide range of applications such as generating high-quality images, video, and audio contents. However, training a GAN could become computationally expensive for large neural networks. In this work, we propose a hybrid quantum-classical architecture for improving GAN (denoted as QC-GAN). The performance was examed numerically by benchmarking with a classical GAN using MindSpore Quantum on the task of hand-written image generation. The generator of the QC-GAN consists of a quantum variational circuit together with a one-layer neural network, and the discriminator consists of a traditional neural network. Leveraging the entangling and expressive power of quantum circuits, our hybrid architecture achieved better performance (Frechet Inception Distance) than the classical GAN, with much fewer training parameters and number of iterations for convergence. We have also demonstrated the superiority of QC-GAN over an alternative quantum GAN, namely pathGAN, which could hardly generate 16$\times$16 or larger images. This work demonstrates the value of combining ideas from quantum computing with machine learning for both areas of Quantum-for-AI and AI-for-Quantum.

arXiv:2402.01791•Feb 2, 2024•4 citations

Quantum generative adversarial network for generating discrete data

Haozhen Situ, Zhimin He, Lvzhou Li +1 more

Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.

•Jul 3, 2018•15 citations

Quantum generative adversarial network for discrete data

Haozhen Situ, Zhimin He, Yuyi Wang +2 more

Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.

•Jul 3, 2018•2 citations

Learning and inference on generative adversarial quantum circuits

Jinfeng Zeng, Yufeng Wu, Jin-Guo Liu +2 more

Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However, training of quantum circuits can be more challenging compared to classical neural networks due to the lack of an efficient differentiable learning algorithm. We devise an adversarial quantum-classical hybrid training scheme via coupling a quantum circuit generator and a classical neural network discriminator together. After training, the quantum circuit generative model can infer missing data with quadratic speed-up via amplitude amplification. We numerically simulate the learning and inference of generative adversarial quantum circuits using the prototypical bars-and-stripes dataset. Generative adversarial quantum circuits are a fresh approach to machine learning which may enjoy the practically useful quantum advantage of near-term quantum devices.

arXiv:1808.03425•Physical Review A•May 6, 2019•94 citations

Adversarial training of quantum Born machine

Haozhen Situ, Zhimin He, Lvzhou Li +1 more

Generative adversarial network (GAN) is an effective machine learning framework to train unsupervised generative models, and has drawn lots of attention in recent years. In the meantime, there are some researches that use parameterized quantum circuits to generate simple patterns. In this paper, we present a quantum version of GAN, where parameterized quantum circuits are trained by an adversarial discriminator, to generate new samples that follows the probability distribution of a given training dataset. Two families of quantum circuits, both composed of simple one-qubit rotation and two-qubit controlled-phase gates, are considered. The parameters are learned through classical gradient descent optimization. The results of a small-scale proof-of-principle numerical experiment demonstrate that quantum circuits can be trained in an adversarial way for generative tasks.

•Jul 3, 2018•2 citations

Experimental demonstration of a quantum generative adversarial network for continuous distributions

Abhinav Anand, Jonathan Romero, Matthias Degroote +1 more

The potential advantage of machine learning in quantum computers is a topic of intense discussion in the literature. Theoretical, numerical and experimental explorations will most likely be required to understand its power. There has been different algorithms proposed to exploit the probabilistic nature of variational quantum circuits for generative modelling. In this paper, we employ a hybrid architecture for quantum generative adversarial networks (QGANs) and study their robustness in the presence of noise. We devise a simple way of adding different types of noise to the quantum generator circuit, and numerically simulate the noisy hybrid QGANs to learn continuous probability distributions, and show that the performance of HQGANs remain unaffected. We also investigate the effect of different parameters on the training time to reduce the computational scaling of the algorithm and simplify its deployment on a quantum computer. We then perform the training on Rigetti's Aspen-4-2Q-A quantum processing unit, and present the results from the training. Our results pave the way for experimental exploration of different quantum machine learning algorithms on noisy intermediate scale quantum devices.

•Jun 2, 2020•10 citations
Abstract A hybrid quantum–classical approach to model continuous classical probability distributions using a variational quantum circuit is proposed. The architecture of this quantum generator consists of a quantum circuit that encodes a classical random variable into a quantum state and a parameterized quantum circuit trained to mimic the target distribution. The model allows for easy interfacing with a classical function, such as a neural network, and is trained using an adversarial learning approach. It is shown that the quantum generator is able to learn using either a classical neural network or a variational quantum circuit as the discriminator model. This implementation takes advantage of automatic differentiation tools to perform the optimization of the variational circuits employed. The framework presented here for the design and implementation of the variational quantum generators can serve as a blueprint for designing hybrid quantum–classical models for other machine learning tasks.
Generative adversarial network (GAN) is one of the widely-adopted machine-learning frameworks for a wide range of applications such as generating high-quality images, video, and audio contents. However, training a GAN could become computationally expensive for large neural networks. In this work, we propose a hybrid quantum-classical architecture for improving GAN (denoted as QC-GAN). The performance was examed numerically by benchmarking with a classical GAN using MindSpore Quantum on the task of hand-written image generation. The generator of the QC-GAN consists of a quantum variational circuit together with a one-layer neural network, and the discriminator consists of a traditional neural network. Leveraging the entangling and expressive power of quantum circuits, our hybrid architecture achieved better performance (Frechet Inception Distance) than the classical GAN, with much fewer training parameters and number of iterations for convergence. We have also demonstrated the superiority of QC-GAN over an alternative quantum GAN, namely pathGAN, which could hardly generate 16$\times$16 or larger images. This work demonstrates the value of combining ideas from quantum computing with machine learning for both areas of Quantum-for-AI and AI-for-Quantum.
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.
Quantum machine learning has recently attracted much attention from the community of quantum computing. In this paper, we explore the ability of generative adversarial networks (GANs) based on quantum computing. More specifically, we propose a quantum GAN for generating classical discrete distribution, which has a classical-quantum hybrid architecture and is composed of a parameterized quantum circuit as the generator and a classical neural network as the discriminator. The parameterized quantum circuit only consists of simple one-qubit rotation gates and two-qubit controlled-phase gates that are available in current quantum devices. Our scheme has the following characteristics and potential advantages: (i) It is intrinsically capable of generating discrete data (e.g., text data), while classical GANs are clumsy for this task due to the vanishing gradient problem. (ii) Our scheme avoids the input/output bottlenecks embarrassing most of the existing quantum learning algorithms that either require to encode the classical input data into quantum states, or output a quantum state corresponding to the solution instead of giving the solution itself, which inevitably compromises the speedup of the quantum algorithm. (iii) The probability distribution implicitly given by data samples can be loaded into a quantum state, which may be useful for some further applications.
Quantum mechanics is inherently probabilistic in light of Born's rule. Using quantum circuits as probabilistic generative models for classical data exploits their superior expressibility and efficient direct sampling ability. However, training of quantum circuits can be more challenging compared to classical neural networks due to the lack of an efficient differentiable learning algorithm. We devise an adversarial quantum-classical hybrid training scheme via coupling a quantum circuit generator and a classical neural network discriminator together. After training, the quantum circuit generative model can infer missing data with quadratic speed-up via amplitude amplification. We numerically simulate the learning and inference of generative adversarial quantum circuits using the prototypical bars-and-stripes dataset. Generative adversarial quantum circuits are a fresh approach to machine learning which may enjoy the practically useful quantum advantage of near-term quantum devices.
Generative adversarial network (GAN) is an effective machine learning framework to train unsupervised generative models, and has drawn lots of attention in recent years. In the meantime, there are some researches that use parameterized quantum circuits to generate simple patterns. In this paper, we present a quantum version of GAN, where parameterized quantum circuits are trained by an adversarial discriminator, to generate new samples that follows the probability distribution of a given training dataset. Two families of quantum circuits, both composed of simple one-qubit rotation and two-qubit controlled-phase gates, are considered. The parameters are learned through classical gradient descent optimization. The results of a small-scale proof-of-principle numerical experiment demonstrate that quantum circuits can be trained in an adversarial way for generative tasks.
The potential advantage of machine learning in quantum computers is a topic of intense discussion in the literature. Theoretical, numerical and experimental explorations will most likely be required to understand its power. There has been different algorithms proposed to exploit the probabilistic nature of variational quantum circuits for generative modelling. In this paper, we employ a hybrid architecture for quantum generative adversarial networks (QGANs) and study their robustness in the presence of noise. We devise a simple way of adding different types of noise to the quantum generator circuit, and numerically simulate the noisy hybrid QGANs to learn continuous probability distributions, and show that the performance of HQGANs remain unaffected. We also investigate the effect of different parameters on the training time to reduce the computational scaling of the algorithm and simplify its deployment on a quantum computer. We then perform the training on Rigetti's Aspen-4-2Q-A quantum processing unit, and present the results from the training. Our results pave the way for experimental exploration of different quantum machine learning algorithms on noisy intermediate scale quantum devices.