Quantum Simulation of Nucleon-Antinucleon Interaction in Large-$N$ QCD$_2$ on an IBM Quantum Nighthawk Processor

We report a quantum simulation of the nucleon--antinucleon interaction in large-$N$ two-dimensional quantum chromodynamics (QCD$_2$) on the IBM Quantum Nighthawk processor. In the large-$N$ limit, QCD$_2$ admits a bosonized description in which baryons emerge as topological solitons (kinks) of an effective mesonic field theory, providing a controlled, nonperturbative framework for baryon--antibaryon dynamics. We formulate the problem by mapping the continuum bosonized Hamiltonian to a spin-chain representation equivalent to an XXZ model with anisotropy set by the QCD parameters. In this mapping, nucleon and antinucleon states correspond to kink and antikink excitations, respectively, while their interaction is encoded in the spin correlations of the chain. Using Jordan--Wigner encoding, we implement the resulting XXZ Hamiltonian on a finite set of qubits and realize it via a variational ground state ansatz and postselected nonunitary disorder operator insertions optimized for the Nighthawk architecture. We then show the kink--antikink interaction potential built from the conditional energies of these nonunitary string operators can be robustly extracted from the quantum hardware due to structured error cancelation. The resulting potential exhibits the expected attractive behavior. The quantum simulation results are benchmarked against exact diagonalization, ideal statevector evaluation showing good agreement. To connect the device result to the continuum field theory, we extract the potential in the continuum limit using large-$L$ matrix product state calculations.

Source: arXiv:2606.02574v1 - http://arxiv.org/abs/2606.02574v1 PDF: https://arxiv.org/pdf/2606.02574v1 Original Link: http://arxiv.org/abs/2606.02574v1