Representation Learning via Quantum Neural Tangent Kernels

Journal Article · Wed Aug 17 00:00:00 EDT 2022 · PRX Quantum

DOI:https://doi.org/10.1103/prxquantum.3.030323· OSTI ID:1982853

Liu, Junyu ^[1]; Tacchino, Francesco ^[2]; Glick, Jennifer R. ^[3]; Jiang, Liang ^[1]; Mezzacapo, Antonio ^[3]

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1. Univ. of Chicago, IL (United States); Chicago Quantum Exchange, IL (United States)
2. IBM Research-Zurich, Rüschlikon (Switzerland)
3. IBM, Yorktown Heights, NY (United States). Thomas J. Watson Research Center

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.

• Research Organization: National Quantum Information Science (QIS) Research Centers (United States). Next Generation Quantum Science and Engineering (Q-NEXT)
• Sponsoring Organization: National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); USDOE
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1982853
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 3 Vol. 3; ISSN 2691-3399
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Machine learning
Physics
Quantum algorithms
Quantum simulation