Experimental Single-Setting Quantum State Tomography

Quantum computers solve ever more complex tasks using steadily growing system sizes. Characterizing these quantum systems is vital, yet becoming increasingly challenging. The gold-standard state tomography (QST), capable of fully reconstructing a without prior knowledge. Measurement and classical computing costs, however, increase exponentially in the size - bottleneck given scale existing near-term devices. Here, we demonstrate scalable practical QST approach that uses single measurement setting, namely symmetric informationally complete (SIC) positive operator-valued measures (POVM). We implement nonorthogonal measurements on an ion trap device by utilizing energy levels each ancilla qubits. More precisely, locally map SIC POVM to orthogonal states embedded higher-dimensional system, which read out repeated in-sequence detections, providing full tomographic information every shot. Combining this with recently developed randomized toolbox ("classical shadows") proves be powerful combination. alleviates need for choosing settings at random ("derandomization"), while shadows enable estimation arbitrary polynomial functions density matrix orders magnitudes faster than standard methods. latter enables in-depth entanglement studies, experimentally showcase 5-qubit absolutely maximally entangled (AME) state. Moreover, fact available shot online real time. 8-qubit state, as well fast identification. All all, features SIC-based shadow highly convenient tool characterization.