Representation Learning via Quantum Neural Tangent Kernels
Abstract
Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.
- Authors:
-
[1];
- Univ. of Chicago, IL (United States); Chicago Quantum Exchange, IL (United States)
- IBM Research-Zurich, Rüschlikon (Switzerland)
- IBM, Yorktown Heights, NY (United States). Thomas J. Watson Research Center
- Publication Date:
- Research Org.:
- National Quantum Information Science (QIS) Research Centers (United States). Next Generation Quantum Science and Engineering (Q-NEXT)
- Sponsoring Org.:
- USDOE; US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); National Science Foundation (NSF)
- OSTI Identifier:
- 1982853
- Grant/Contract Number:
- AC02-06CH11357; FA9550-21-1-0209; W911NF-18-1-0020; W911NF-18-1-0212; W911NF-16-1-0349; FA9550-19-1-0399; EFMA-1640959; OMA-1936118; EEC-1941583
- Resource Type:
- Accepted Manuscript
- Journal Name:
- PRX Quantum
- Additional Journal Information:
- Journal Volume: 3; Journal Issue: 3; Journal ID: ISSN 2691-3399
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Machine learning; Quantum algorithms; Quantum simulation
Citation Formats
Liu, Junyu, Tacchino, Francesco, Glick, Jennifer R., Jiang, Liang, and Mezzacapo, Antonio. Representation Learning via Quantum Neural Tangent Kernels. United States: N. p., 2022.
Web. doi:10.1103/prxquantum.3.030323.
Liu, Junyu, Tacchino, Francesco, Glick, Jennifer R., Jiang, Liang, & Mezzacapo, Antonio. Representation Learning via Quantum Neural Tangent Kernels. United States. https://doi.org/10.1103/prxquantum.3.030323
Liu, Junyu, Tacchino, Francesco, Glick, Jennifer R., Jiang, Liang, and Mezzacapo, Antonio. Wed .
"Representation Learning via Quantum Neural Tangent Kernels". United States. https://doi.org/10.1103/prxquantum.3.030323. https://www.osti.gov/servlets/purl/1982853.
@article{osti_1982853,
title = {Representation Learning via Quantum Neural Tangent Kernels},
author = {Liu, Junyu and Tacchino, Francesco and Glick, Jennifer R. and Jiang, Liang and Mezzacapo, Antonio},
abstractNote = {Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.},
doi = {10.1103/prxquantum.3.030323},
journal = {PRX Quantum},
number = 3,
volume = 3,
place = {United States},
year = {Wed Aug 17 00:00:00 EDT 2022},
month = {Wed Aug 17 00:00:00 EDT 2022}
}
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