Proof-of-principle reconstruction and geometric benchmarking of 3-qubit pure states on ibm_osaka

We report a proof-of-principle experimental demonstration of the reconstruction and geometric benchmarking of three-qubit pure states on IBM’s 127-qubit superconducting quantum processor, ibm_osaka. Focusing on the three-qubit W state, we exploit the theoretical result that almost all pure 3-qubit states are uniquely determined by any two of their two-qubit reduced density matrices. Using a 7-setting quantum state tomography protocol, we reconstruct 2-qubit marginal states so as to obtain the parent 3-qubit state. We further employ quantum steering ellipsoids to geometrically visualize the reconstructed subsystems. The experimentally obtained ellipsoid semi-axes lengths, centers and normalized volumes show good agreement with the theoretical predictions, demonstrating the usefulness of geometric benchmarking tools in the NISQ era.