Fig. 4: Enhancing experimental detection of \({{\mathbb{Z}}}_{2}\) spin liquid.
From: Enhancing detection of topological order by local error correction
a, d In the experiment28, 219 qubits are placed on the links of a kagome lattice. Upon applying LED, the Z and X closed-loop observables are amplified for certain ranges of Δ/Ω. The shaded purple regions show the support of large, decorated Wilson loops after one layer of correction with n = 1. b, e Expectation value of Wilson loops depicted in (a, c) for different correction layers n. Plotted error bars (shaded regions) show expected variation (one standard error) of the mean. The regime in which both types of loops are amplified corresponds nicely to the spin-liquid regime identified in ref. 28 (shaded blue region). c, f The behavior of expectation values of open Z- and X-strings under LED further confirms our findings, as both types of open strings stay at 0 in the spin-liquid regime. Here, the measured open strings are half of the Wilson loops. By considering the behavior of all types of loops and strings---closed and open, Z and X---we find that there are four regimes (I-IV), corresponding to four phases: (I) Z-paramagnet, (II) X-paramagnet, (III) topological spin liquid (blue), and (IV) a phase which is consistent with strong decoherence effects (gray). In our analysis, the progression from Regime (III) to (IV) appears to be smooth.
