The formulation of the theory on a spacetime lattice provides a non-perturbative regularization of the theory with the lattice spacing playing the role of an inverse UV cutoff. Lattice gauge theory (LGT) 3 is a mature and successful discretisation strategy for computational methods that have developed into an extremely successful field of science. There are also suggestions of non-Abelian forces beyond the Standard Model (BSM) that are completely separate from QCD and might, for example, underlie the Higgs sector of the Standard Model 1 or provide a strongly interacting theory for dark matter 2. The most prominent example, quantum chromodynamics (QCD), is a non-Abelian gauge theory that explains the strong interactions between quarks and gluons and ultimately underlies nuclear physics. Within this area, quantum computation of non-Abelian gauge theories is an outstanding challenge. Prime candidates for the application of such quantum simulations are gauge theories, which play a major role in many branches of physics and comprise the entire Standard Model of particle physics. Quantum computing technologies are developing quickly in recent years with applications in a broad range of scientific areas from chemistry to fundamental interactions of Nature. 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. 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. 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. This enables the observation of hadrons and the calculation of their associated masses. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions.
Quantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories.
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