Variational Quantum Algorithms (VQA)

Abstract
“Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications, although fault-tolerant quantum computers will likely not be available for several years. Currently available quantum devices have serious constraints, including limited qubit numbers and noise processes that limit circuit depth. Variational Quantum Algorithms (VQAs), which employ a classical optimizer to train a parametrized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisioned for quantum computers, and they appear to the best hope for obtaining quantum advantage. Nevertheless, challenges remain including the trainability, accuracy, and efficiency of VQAs. In this review article we present an overview of the field of VQAs. Furthermore, we discuss strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage.

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M. Cerezo,1, 2, 3 Andrew Arrasmith,1 Ryan Babbush,4 Simon C. Benjamin,5 Suguru Endo,6 Keisuke Fujii,7, 8, 9 Jarrod R. McClean,4 Kosuke Mitarai,7, 10, 11 Xiao Yuan,12, 13 Lukasz Cincio,1, 3 and Patrick J. Coles1, 3

1-Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 
2-Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA
3-Quantum Science Center, Oak Ridge, TN 37931, USA
4-Google Quantum AI Team, Venice, CA 90291, United States of America
5-Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
6-NTT Secure Platform Laboratories, NTT Corporation, Musashino, Tokyo 180-8585, Japan
7-Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
8-Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Osaka 560-8531, Japan
9-Center for Emergent Matter Science, RIKEN, Saitama 351-0198, Japan
10-Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka 560-8531, Japan
11J-ST, PRESTO, Saitama 332-0012, Japan 12Center on Frontiers of Computing Studies, Department of Computer Science, Peking University, Beijing 10087