Penalty methods for a variational quantum eigensolver

The variational quantum eigensolver (VQE) is a promising algorithm to compute eigenstates and eigenenergies of given system that can be performed on near-term computer. Obtaining in specific symmetry sector the often necessary for practical applications VQE various fields ranging from high-energy physics chemistry. It common add penalty term cost function calculate such symmetry-resolving energy spectrum; however, systematic analysis effect has been lacking, use not justified rigorously. In this paper, we investigate two major types terms were proposed previous studies. We show one works properly obtained by with reside desired sector. further give convenient formula determine magnitude term, which may lead faster convergence VQE. Meanwhile, prove other type does work obtaining target state rigorous sense even gives completely wrong results some cases. finally provide numerical simulations validate our analysis. Our apply general systems lay theoretical foundation obtain spectrum system, fuels application computer.Received 29 October 2020Revised 13 January 2021Accepted 21 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013197Published American Physical Society under Creative Commons Attribution 4.0 International license. Further distribution must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum algorithmsQuantum simulationTechniquesSymmetries condensed matterQuantum InformationCondensed Matter, Materials & Applied Physics