Fig. 3: SU(3) thermal states for a unit cell with trapped ions.
From: The phase diagram of quantum chromodynamics in one dimension on a quantum computer
a Chiral condensate for a unit cell obtained from exact diagonalization (ED) for x = 1.0, m = 0.5. The phase diagram is qualitatively similar to Fig. 2a, but differs quantitatively, with the transition point at zero temperature occurring at a distinct μ-value compared to SU(2). b Classical simulation results for our variational quantum eigensolver (VQE) protocol (Fig. 1) in the noiseless case. c The VQE experiment is run for μ = 2 close to the phase transition, allowing up to 350 cost function evaluations. The experimental result matches well with the noisy VQE simulation, showing the effectiveness of the ansatz in preparing the thermal state near the transition. Additionally, the VQE circuit is run using the optimised ideal VQE parameters for T = 0.5 for a range of μ values, confirming our noise model. The spread of the noisy VQE simulation collected over twenty trials (represented by the error bar with the box denoting the interquartile range) highlights the reliability of our protocol. Error bars for the experimental VQE and direct implementation points show one standard deviation for repeated trials with parameters obtained from the VQE run. d Boltzmann weights of eigenstates of the Hamiltonian in the charge-singlet thermal state are shown at three different chemical potentials, highlighting the transition from vacuum-dominated density matrix to baryon-dominated density matrix. e, f show the strong coupling (x ≪ 1) and physical eigenstates. Due to the presence of three colours, the unit cell allows for more gauge-invariant states than the SU(2) model in Fig. 2, which did not include the tetraquark state.
