SU(2) hadrons on a quantum computer

Quantum computers can dramatically enhance current simulation methods. Some of the most promising applications are non-Abelian gauge theories that describe fundamental particle interactions. In particular quantum chromodynamics (QCD), which describes the strong interaction between quarks and gluons that form hadrons such as protons and neutrons, is relying on future quantum computers to perform simulations that are known to be unattainable on classical computers. Here, we present the first quantum computer simulation of a complete non-Abelian gauge theory incorporating both gauge and matter fields. We investigate the SU(2) gauge theory in one dimension - with two color degrees of freedom - as a first important step towards studying QCD. A striking signature of the non-Abelian nature of the model is that the spectrum contains not only meson-type states, made of one valence fermion and one valence antifermion, but also baryon-type states composed of only valence fermions. We performed a quantum computation of the masses of the lightest baryon and meson in the theory on an IBM superconducting platform using a variational quantum eigensolver. Running the full SU(2) theory on current quantum hardware was enabled by a resource-efficient approach that lays out the premises for future quantum simulations of more complex and ultimately sign-problem afflicted models.