Fig. 2: Toric code ground state preparation.
From: Topological order from measurements and feed-forward on a trapped ion quantum computer
a Definition of the stabilizer operators (1) on the unraveled torus. Numbers denote the different ions and specify the boundary conditions. Plaquettes are labeled by their upper left qubits. The state comprises 4 × 4 qubits and periodic boundary conditions. b Logical Z string operators are Zhori = Z0Z1Z2Z3 (Zvert = Z0Z4Z8Z12) and their vertical (horizontal) translations. \(\overline{{Z}^{{{{{{{{\rm{hori}}}}}}}}}}\) and \(\overline{{Z}^{{{{{{{{\rm{vert}}}}}}}}}}\) denote expectation values of the logical string operators, averaged over translations. c Expectation values of the stabilizers obtained from collapsing the wavefunction in the single-qubit X- and Z-bases. Error bars denote one standard error on the mean. d Entanglement entropy measurement on 2 × 2 (top) and 2 × 3 regions (bottom). Colored bars denote \({S}_{X}^{(2)}\) for different subsystems of a region with shapes as shown in the inset and γ is defined in Eq. (2). Dashed lines show exact values. Error bars denote one standard error on the mean. The maximum error in the estimates of \({S}_{X}^{(2)}\) for 2 × 2 (2 × 3) regions is ±0.056 (±0.091). Hatched white bars denote average topological entanglement entropies.
