Trainability of Dissipative Perceptron-Based Quantum Neural Networks

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. He...

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Vydáno v:Physical review letters Ročník 128; číslo 18; s. 180505
Hlavní autoři: Sharma, Kunal, Cerezo, M., Cincio, Lukasz, Coles, Patrick J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States American Physical Society (APS) 06.05.2022
Témata:
artificial neural networks
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
machine learning
quantum algorithms
quantum computation
quantum information processing
quantum networks
ISSN:0031-9007, 1079-7114, 1079-7114
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Shrnutí:Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we call dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed. Our work represents the first rigorous analysis of the scalability of a perceptron-based QNN.
Bibliografie:ObjectType-Article-1
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USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
89233218CNA000001
LA-UR-20-23484
USDOE Laboratory Directed Research and Development (LDRD) Program
ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.128.180505