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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| Published in: | Physical review letters Vol. 128; no. 18; p. 180505 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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United States
American Physical Society (APS)
06.05.2022
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| Subjects: | |
| ISSN: | 0031-9007, 1079-7114, 1079-7114 |
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| Abstract | 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. |
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| AbstractList | 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. 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. Here our work represents the first rigorous analysis of the scalability of a perceptron-based QNN. 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.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. |
| ArticleNumber | 180505 |
| Author | Cincio, Lukasz Cerezo, M. Coles, Patrick J. Sharma, Kunal |
| Author_xml | – sequence: 1 givenname: Kunal orcidid: 0000-0003-3132-1088 surname: Sharma fullname: Sharma, Kunal – sequence: 2 givenname: M. orcidid: 0000-0002-2757-3170 surname: Cerezo fullname: Cerezo, M. – sequence: 3 givenname: Lukasz orcidid: 0000-0002-6758-4376 surname: Cincio fullname: Cincio, Lukasz – sequence: 4 givenname: Patrick J. surname: Coles fullname: Coles, Patrick J. |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/35594093$$D View this record in MEDLINE/PubMed https://www.osti.gov/servlets/purl/1992248$$D View this record in Osti.gov |
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| SubjectTerms | artificial neural networks CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS machine learning quantum algorithms quantum computation quantum information processing quantum networks |
| Title | Trainability of Dissipative Perceptron-Based Quantum Neural Networks |
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