Fig. 5: Prediction of subsystem purity in the AKLT resource state using RSS.
From: Demonstration of robust and efficient quantum property learning with shallow shadows
a We demonstrate how the RSS method can use a single dataset to concurrently predict the purity of all subsystems up to two qubits within AKLT resource states. We show theoretical predictions (left), experimental results with error mitigation (center), and the residual difference between mitigated and unmitigated results (right). The residual plot reveals that error mitigation systematically increases the predicted purities, bringing them closer to theoretical values, with the strongest corrections appearing in the three distinct AKLT clusters. The values at (i, j) represent the purity of the reduced density matrix \({{\rm{Tr}}}({\rho }_{ij}^{2})\). The AKLT resource state has three clusters, each representing a smaller AKLT state with two spin-1 particles before fusion measurement; experimental predictions clearly show this pattern as well, and closely align with theoretical predictions. b We show a schematic of the AKLT resource state before fusion measurements are applied to prepare the AKLT state.
