Fig. 2: SU(2) thermal states for a unit cell with trapped ions.
From: The phase diagram of quantum chromodynamics in one dimension on a quantum computer
a Exact diagonalization (ED) results for the SU(2) unit cell for x = 1 and m = 0.5. The order parameter \({\langle \hat{\chi }\rangle }_{0}\) (chiral condensate) takes large negative values in the low T and μ limit. Chiral symmetry \({\langle \hat{\chi }\rangle }_{0}\)= 0 is restored at high μ and T → ∞. b Classical simulation results for our variational quantum eigensolver (VQE) protocol (Fig. 1) for the noise-free case. c Experimental data for T = 0.5 (dashed line in a). Our motional ancillae based protocol uses up to 230 cost function evaluations per point, determining the chiral condensate for five distinct chemical potential values. The experimental VQE results (red diamonds) are in good agreement with both the ED (black curve) and noisy simulation results (grey boxes). The grey boxes show the spread of mean chiral condensate values from twenty noisy VQE runs (represented by the error bar with the box denoting the inter-quartile range) for each chemical potential, highlighting the protocol’s high success rate. Error bars for the experimental VQE points show one standard deviation for repeated trials with parameters obtained from the VQE run. d Composition of the charge-singlet thermal state at varying chemical potentials. The mixtures of SU(2) physical eigenstates show the transition from a vacuum-dominated to a baryon-dominated phase. f shows the composition of the physical eigenstates in terms of the strong coupling (x ≪ 1) eigenstates (e). The heights of the various bar-segments represent the contributions of the strong-coupling states.
