Quantum chromodynamics - the theory of quarks and gluons - has been known for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, that opened a new research field. Crucially, numerous unsolved questions of the standard model can exclusively be addressed by non-perturbative calculations. Quantum computers can solve problems for which well established QCD methods are inapplicable, such as real-time evolution. We take a keystep in exploring this possibility by performing a real-time evolution of tetraquark and pentaquark physics in one-dimensional SU(3) gauge theory on a superconducting quantum computer. Our experiment represents a first quantum computation involving quarks with three colour degrees of freedom, i.e. with the gauge group of QCD.