Out-of-distribution generalization for learning quantum dynamics
Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution...
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| Veröffentlicht in: | Nature communications Jg. 14; H. 1; S. 3751 - 9 |
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05.07.2023
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| Abstract | Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.
Generalization - that is, the ability to extrapolate from training data to unseen data - is fundamental in machine learning, and thus also for quantum ML. Here, the authors show that QML algorithms are able to generalise the training they had on a specific distribution and learn over different distributions. |
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| AbstractList | Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Generalization - that is, the ability to extrapolate from training data to unseen data - is fundamental in machine learning, and thus also for quantum ML. Here, the authors show that QML algorithms are able to generalise the training they had on a specific distribution and learn over different distributions. Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Abstract Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Generalization - that is, the ability to extrapolate from training data to unseen data - is fundamental in machine learning, and thus also for quantum ML. Here, the authors show that QML algorithms are able to generalise the training they had on a specific distribution and learn over different distributions. |
| ArticleNumber | 3751 |
| Author | Sornborger, Andrew T. Cincio, Lukasz Ezzell, Nicholas Gibbs, Joe Coles, Patrick J. Caro, Matthias C. Holmes, Zoë Huang, Hsin-Yuan |
| Author_xml | – sequence: 1 givenname: Matthias C. orcidid: 0000-0001-9009-2372 surname: Caro fullname: Caro, Matthias C. email: matthias.caro@fu-berlin.de organization: Department of Mathematics, Technical University of Munich, Munich Center for Quantum Science and Technology (MCQST), Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Institute for Quantum Information and Matter, Caltech – sequence: 2 givenname: Hsin-Yuan orcidid: 0000-0001-5317-2613 surname: Huang fullname: Huang, Hsin-Yuan organization: Institute for Quantum Information and Matter, Caltech, Department of Computing and Mathematical Sciences, Caltech – sequence: 3 givenname: Nicholas orcidid: 0000-0002-4983-0617 surname: Ezzell fullname: Ezzell, Nicholas organization: Information Sciences, Los Alamos National Laboratory, Department of Physics & Astronomy, University of Southern California – sequence: 4 givenname: Joe surname: Gibbs fullname: Gibbs, Joe organization: Department of Physics, University of Surrey, AWE, Aldermaston – sequence: 5 givenname: Andrew T. surname: Sornborger fullname: Sornborger, Andrew T. organization: Information Sciences, Los Alamos National Laboratory – sequence: 6 givenname: Lukasz surname: Cincio fullname: Cincio, Lukasz organization: Theoretical Division, Los Alamos National Laboratory – sequence: 7 givenname: Patrick J. surname: Coles fullname: Coles, Patrick J. organization: Theoretical Division, Los Alamos National Laboratory, Normal Computing Corporation – sequence: 8 givenname: Zoë surname: Holmes fullname: Holmes, Zoë organization: Information Sciences, Los Alamos National Laboratory, Institute of Physics, Ecole Polytechnique Fédéderale de Lausanne (EPFL) |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/37407571$$D View this record in MEDLINE/PubMed https://www.osti.gov/biblio/1988191$$D View this record in Osti.gov |
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| Snippet | Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees... Abstract Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established... |
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| SubjectTerms | 639/705/117 639/766/483/481 Algorithms CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Entangled states Humanities and Social Sciences Learning algorithms Machine learning multidisciplinary Neural networks Quantum entanglement Quantum Information Science and Technology Quantum theory Qubits (quantum computing) Science Science (multidisciplinary) Training |
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| Title | Out-of-distribution generalization for learning quantum dynamics |
| URI | https://link.springer.com/article/10.1038/s41467-023-39381-w https://www.ncbi.nlm.nih.gov/pubmed/37407571 https://www.proquest.com/docview/2833382647 https://www.proquest.com/docview/2833997681 https://www.osti.gov/biblio/1988191 https://pubmed.ncbi.nlm.nih.gov/PMC10322910 https://doaj.org/article/70f24e87b63943c980a107a5799fddd6 |
| Volume | 14 |
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