Simulations of energy loss and hadronization are essential for understanding a range of phenomena in non-equilibrium strongly-interacting matter. We establish a framework for performing such simulations on a quantum computer and apply it to a heavy quark moving across a modest-sized 1+1D SU(2) lattice of light quarks. Conceptual advances with regard to simulations of non-Abelian versus Abelian theories are developed, allowing for the evolution of the energy in light quarks, of their local non-Abelian charge densities, and of their multi-partite entanglement to be computed. The non-trivial action of non-Abelian charge operators on arbitrary states suggests mapping the heavy quarks to qubits alongside the light quarks, and limits the heavy-quark motion to discrete steps among spatial lattice sites. Further, the color entanglement among the heavy quarks and light quarks is most simply implemented using hadronic operators, and Domain Decomposition is shown to be effective in quantum state preparation. Scalable quantum circuits that account for the heterogeneity of non-Abelian charge sectors across the lattice are used to prepare the interacting ground-state wavefunction in the presence of heavy quarks. The discrete motion of heavy quarks between adjacent spatial sites is implemented using fermionic SWAP operations. Quantum simulations of the dynamics of a system on L=3 spatial sites are performed using IBM’s ibm_pittsburgh quantum computer using 18 qubits, for which the circuits for state preparation, motion, and one second-order Trotter step of time evolution have a two-qubit depth of 398 after transpilation. A suite of error mitigation techniques are used to extract the observables from the simulations, providing results that are in good agreement with classical simulations. The framework presented here generalizes straightforwardly to other non-Abelian groups, including SU(3) for quantum chromodynamics.

We would like to thank Roland Farrell, Henry Froland and Nikita Zemlevskiy for helpful discussions. This work was supported, in part, by U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science, by the Quantum Science Center (QSC) which is a National Quantum Information Science Research Center of the U.S Department of Energy, and by PNNL’s Quantum Algorithms and Architecture for Domain Science (QuAADS) Laboratory Directed Research and Development (LDRD) Initiative. The Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05 76RL01830. It was also supported, in part, by the Department of Physics and the College of Arts and Sciences at the University of Washington. This research used resources of the Oak Ridge Leadership Computing Facility (OLCF), which is a DOE Office of Science User Facility supported under Contract DE AC05-00OR22725. We acknowledge the use of IBM Quantum services for this work. The views expressed are those of the authors, and do not reflect the official policy or position of IBM or the IBM Quantum team. This work was enabled, in part, by the use of advanced computational, storage and networking infrastructure provided by the Hyak supercomputer system at the University of Washington. We have made extensive use of Wolfram Mathematica, python, julia, jupyter notebooks in the Conda environment, and IBM’s quantum programming environment qiskit. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award NP-ERCAP0032083.