Equivariant quantum circuits for learning on weighted graphs

Skolik, Andrea; Cattelan, Michele; Yarkoni, Sheir; Bäck, Thomas; Dunjko, Vedran

doi:10.48550/arxiv.2205.06109

Cited by 8 publications

(14 citation statements)

References 41 publications

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“…Geometric quantum machine learning is a new and exciting field which seeks to produce helpful inductive biases for quantum machine learning models based on the symmetries of the problem at hand. While there already exist several proposals in the literature within the field of GQML [44][45][46][47][48][49], these mainly deal with unitary models which maintain the same group representation throughout the computation. In this work, we generalize previous results and we present a theoretical framework to understand, design, and optimize over general equivariant channels, which we refer to as EQNNs.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…In [44] and [45] the authors lay theoretical ground work for the integration of symmetries into QML. Methods for constructing equivariant quantum circuits for graph problems were given in [46,47,49,91]. In addition, [48,92] established a connection between SU(d)-equivariant QNNs and the permutational quantum computing model [93], showing that SU(d)-equivariant QNNs are in general not classically simulable.…”

Section: B Equivariance In Quantum Informationmentioning

confidence: 99%

“…Equivariant quantum circuits have been proposed and used in previous works [45][46][47][48][49] mostly in the context of graph problems. However, we note that these fall into standard layers and our framework provides more flexibility as the operations need not be unitary.…”

Section: Standard Embedding and Poolingmentioning

confidence: 99%

“…For instance, when classifying between states presenting a large, or a low, amount of multipartite entanglement [24,42,43], it is natural to employ models whose outputs remain invariant under the action of any local unitary [44]. While recent proposals have started to reveal the power of GQML [44][45][46][47][48][49], the field is still in Figure 1. Schematic representation of our main results.…”

Section: Introductionmentioning

confidence: 99%

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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: Discussion and Outlookmentioning

confidence: 99%

Section: B Equivariance In Quantum Informationmentioning

confidence: 99%

Section: Standard Embedding and Poolingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Theory for Equivariant Quantum Neural Networks

Nguyen¹,

Schatzki²,

Paolo³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For example, in quantum chemistry, some proposals of variational eigensolvers have used the natural symmetry of some molecular to reduce the required number of qubits [57][58][59]. In quantum machine learning, the concept of decomposing Hamiltonian by its symmetric property can be leveraged to design powerful Hamiltonian-based quantum neural networks with some invariant properties [60,61]. In this way, these QNNs can attain better convergence and generalization [62][63][64][65][66].…”

Section: Discussionmentioning

confidence: 99%

QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines

Zhou¹,

Du²,

Tian³

et al. 2022

Preprint

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Deep learning optimal quantum annealing schedules for random Ising models

Hegde

Passarelli²,

Cantele³

et al. 2023

New J. Phys.

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A crucial step in the race towards quantum advantage is optimizing quantum annealing using ad-hoc annealing schedules. Motivated by recent progress in the field, we propose to employ long-short term memory (LSTM) neural networks to automate the search for optimal annealing schedules for random Ising models on regular graphs. By training our network using locally-adiabatic annealing paths, we are able to predict optimal annealing schedules for unseen instances and even larger graphs than those used for training. 

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Equivariant quantum circuits for learning on weighted graphs

Cited by 8 publications

References 41 publications

Theory for Equivariant Quantum Neural Networks

Theory for Equivariant Quantum Neural Networks

QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines

Deep learning optimal quantum annealing schedules for random Ising models

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