Challenges and opportunities in quantum machine learning

Cerezo, M.; Verdon, Guillaume; Huang, Hsin-Yuan; Cincio, Łukasz; Coles, Patrick J.

doi:10.1038/s43588-022-00311-3

Cited by 218 publications

(71 citation statements)

References 92 publications

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“…Recently, some of the ideas of geometric deep learning have been imported to the field of quantum machine learning (QML) [15][16][17][18][19]. QML has become a rapidly growing framework to make practical use of noisy intermediate-scale quantum devices [20].…”

Section: Introductionmentioning

confidence: 99%

Theory for Equivariant Quantum Neural Networks

Nguyen¹,

Schatzki²,

Paolo³

et al. 2022

Preprint

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Most currently used quantum neural network architectures have little-to-no inductive biases, leading to trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in classical machine learning address this crux by creating models encoding the symmetries of the learning task. This is materialized through the usage of equivariant neural networks whose action commutes with that of the symmetry. In this work, we import these ideas to the quantum realm by presenting a general theoretical framework to understand, classify, design and implement equivariant quantum neural networks. As a special implementation, we show how standard quantum convolutional neural networks (QCNN) can be generalized to group-equivariant QCNNs where both the convolutional and pooling layers are equivariant under the relevant symmetry group. Our framework can be readily applied to virtually all areas of quantum machine learning, and provides hope to alleviate central challenges such as barren plateaus, poor local minima, and sample complexity.

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Section: Introductionmentioning

confidence: 99%

Theory for Equivariant Quantum Neural Networks

Nguyen¹,

Schatzki²,

Paolo³

et al. 2022

Preprint

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“…It also remains an open question how our uncertainty treatment can be translated to related concepts like Owen values [34] or Banzhaf-Owen values [35]. Finally, quantum machine learning [36] is a particularly promising field of application beyond XML because randomness is an inherent property of quantum systems.…”

Section: Discussionmentioning

confidence: 99%

Shapley Values with Uncertain Value Functions

Heese¹,

Sascha²,

Jakobs³

et al. 2023

Preprint

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We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random effects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational effort.

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“…Ontic state distributions and ontic response functions for preparation and effect densities are defined using the same additivity relations as (7), (9),…”

Section: Ontological Modelsmentioning

confidence: 99%

“…One of the central challenges facing quantum machine learning is to identify data structures that can be encoded usefully into quantum learning models; in other words, what are the forms of inductive bias that naturally lend themselves to quantum computation [8,9,10,11]? In answering this question, we should be wary of hoping for a one-size-fits-all approach in which Figure 1: A.…”

Section: Introductionmentioning

confidence: 99%

Contextuality and inductive bias in quantum machine learning

Bowles¹,

Wright²,

Farkas³

et al. 2023

Preprint

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Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the types of data structures that lend themselves naturally to quantum models. In this work we look to quantum contextuality-a form of nonclassicality with links to computational advantage-for answers to this question. We introduce a framework for studying contextuality in machine learning, which leads us to a definition of what it means for a learning model to be contextual. From this, we connect a central concept of contextuality, called operational equivalence, to the ability of a model to encode a linearly conserved quantity in its label space. A consequence of this connection is that contextuality is tied to expressivity: contextual model classes that encode the inductive bias are generally more expressive than their noncontextual counterparts. To demonstrate this, we construct an explicit toy learning problem-based on learning the payoff behaviour of a zero-sum game-for which this is the case. By leveraging tools from geometric quantum machine learning, we then describe how to construct quantum learning models with the associated inductive bias, and show through our toy problem that they outperform their corresponding classical surrogate models. This suggests that understanding learning problems of this form may lead to useful insights about the power of quantum machine learning.

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Challenges and opportunities in quantum machine learning

Cited by 218 publications

References 92 publications

Theory for Equivariant Quantum Neural Networks

Theory for Equivariant Quantum Neural Networks

Shapley Values with Uncertain Value Functions

Contextuality and inductive bias in quantum machine learning

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