Enhancing Generative Models via Quantum Correlations

Gao, Xun; Anschuetz, Eric R.; Wang, Shengtao; Cirac, J. Ignacio; Lukin, Mikhail D.

doi:10.1103/physrevx.12.021037

Cited by 25 publications

(18 citation statements)

References 69 publications

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“…Concretely, Ref. [273] proved a theoretical proof of expressivity enhancement from Bayesian networks to their quantum counterpart. Moreover, Du et al [274] analyzed the generalization of QCBMs and QGANs under the maximum mean discrepancy loss and demonstrated the potential advantages of these QGLMs.…”

Section: Challengesmentioning

confidence: 99%

Recent Advances for Quantum Neural Networks in Generative Learning

Tian¹,

Sun²,

Du³

et al. 2022

Preprint

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Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relation and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

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Section: Challengesmentioning

confidence: 99%

Recent Advances for Quantum Neural Networks in Generative Learning

Tian¹,

Sun²,

Du³

et al. 2022

Preprint

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“…Here, we show via simple arguments that access to a more expressive "quantum" space of functions or data is only advantageous when one can efficiently optimize or search over that space. Indeed, there are known results on expressivity advantages of quantum models over classical models [35], and certain learning settings where there is known to exist a quantum advantage in the data needed to learn [43,1]. Just as in classical machine learning, algorithms are tasked with minimizing some risk: R(f…”

Section: Preliminaries 21 Quantum Machine Learningmentioning

confidence: 99%

“…Indeed, in certain regimes [34], training algorithms exist such that the resulting quantum model provably outperforms certain classical algorithms. This would potentially enable the use of quantum models to efficiently represent complex distributions which are provably inefficient to express using classical networks [35].…”

Section: Introduction 1motivationmentioning

confidence: 99%

Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps

Anschuetz¹,

Kiani²

2022

Preprint

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One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that unlike the case in classical neural networks, variational quantum models are often not trainable. The most studied phenomenon is the onset of barren plateaus in the training landscape of these quantum models, typically when the models are very deep. This focus on barren plateaus has made the phenomenon almost synonymous with the trainability of quantum models. Here, we show that barren plateaus are only a part of the story. We prove that a wide class of variational quantum models-which are shallow, and exhibit no barren plateus-have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known. We also study the trainability of variational quantum algorithms from a statistical query framework, and show that noisy optimization of a wide variety of quantum models is impossible with a sub-exponential number of queries. Finally, we numerically confirm our results on a variety of problem instances. Though we exclude a wide variety of quantum algorithms here, we give reason for optimism for certain classes of variational algorithms and discuss potential ways forward in showing the practical utility of such algorithms.

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“…QML proposals most commonly mention quantum entanglement as resource for the potential quantum advantage [5][6][7]. However, quantum entanglement does not encompass all forms of quantum correlation in mixed states.…”

Section: Introductionmentioning

confidence: 99%

The Power of One Clean Qubit in Supervised Machine Learning

Karimi¹,

Javadi-Abhari²,

Simon³

et al. 2022

Preprint

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The field of machine learning could benefit from quantum-enabled devices, as quantum correlations may allow for the discovery of new patterns within large datasets. Thus far, the quantum machine learning literature has mainly focused on entanglement as a resource. The purpose of this paper is to examine the use of quantum coherence and a less studied type of quantum correlation, quantum discord, in machine learning. Our study is based on a non-universal quantum computing model known as deterministic quantum computing with one qubit (DQC1). A simple relationship is shown between coherence consumption and the kernel function, a crucial machine learning concept. We present an implementation of a binary classification problem on IBM hardware using the DQC1 model. Further, we analyze the role of quantum coherence and hardware noise in our implementation.

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Enhancing Generative Models via Quantum Correlations

Cited by 25 publications

References 69 publications

Recent Advances for Quantum Neural Networks in Generative Learning

Recent Advances for Quantum Neural Networks in Generative Learning

Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps

The Power of One Clean Qubit in Supervised Machine Learning

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