SU(2) hadrons on a quantum computer via a variational approach

Yasar Y Atas; Jinglei Zhang; Randy Lewis; Amin Jahanpour; Jan F Haase; Christine A Muschik

doi:10.1038/s41467-021-26825-4

SU(2) hadrons on a quantum computer via a variational approach

Nat Commun. 2021 Nov 11;12(1):6499. doi: 10.1038/s41467-021-26825-4.

Authors

Yasar Y Atas^#^{1

2}, Jinglei Zhang^#^{3

4}, Randy Lewis⁵, Amin Jahanpour^{6

7}, Jan F Haase^{8

9

10}, Christine A Muschik^{6

7

11}

Affiliations

¹ Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1. yyatas@uwaterloo.ca.
² Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1. yyatas@uwaterloo.ca.
³ Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1. jingleizl@gmail.com.
⁴ Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1. jingleizl@gmail.com.
⁵ Department of Physics and Astronomy, York University, Toronto, ON, Canada, M3J 1P3.
⁶ Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
⁷ Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1.
⁸ Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada, N2L 3G1. jan.frhaase@gmail.com.
⁹ Department of Physics & Astronomy, University of Waterloo, Waterloo, ON, Canada, N2L 3G1. jan.frhaase@gmail.com.
¹⁰ Institut für Theoretische Physik und IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany. jan.frhaase@gmail.com.
¹¹ Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada, N2L 2Y5.

^# Contributed equally.

Abstract

Quantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.