Two color 1D-QCD phase diagram on a trapped-ion quantum computer

The phase diagram of Quantum Chromodynamics (QCD) represents a crucial yet challenging target in modern physics. Traditional lattice gauge theory (LGT) methods struggle to simulate this phase diagram at finite chemical potential due to the sign problem. However, emerging quantum simulation techniques offer a potential solution. In this work, we take a significant first step towards investigating the phase diagram of non-abelian gauge theories. We focus on a two-color SU(2) non-abelian gauge theory in one dimension and develop a protocol, using a variational algorithm and group projection technique, to prepare the Gibbs thermal ensemble at finite density while preserving gauge invariance -- allowing us to explore the phase diagram in 1D. By using motional modes of a trapped-ion system as ancilla qubits, we experimentally demonstrate the feasibility of our protocol. Additionally, we investigate the potential for experimentally probing the phase diagram of the SU(3) LGT in one dimension.