  We realize, for the first time, a non-Abelian gauge theory with both gauge
and matter fields 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. Quantum computers are able to create important new
opportunities for ongoing essential research on gauge theories by providing
simulations that are unattainable on classical computers. 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 resource-efficient
approach that not only allows the implementation of a full SU(2) gauge theory
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.
