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Generalized measurements, also called positive operator-valued measures(POVMs), can offer advantages over projective measurements in various quantuminformation tasks. Here, we realize a generalized measurement of one and twosuperconducting qubits with high fidelity and in a single experimental setting.To do so, we propose a hybrid method, the "Naimark-terminated binary tree,"based on a hybridization of Naimark's dilation and binary tree techniques thatleverages emerging hardware capabilities for mid-circuit measurements andfeed-forward control. Furthermore, we showcase a highly effective use ofapproximate compiling to enhance POVM fidelity in noisy conditions. We arguethat our hybrid method scales better toward larger system sizes than itsconstituent methods and demonstrate its advantage by performing detectortomography of symmetric, informationally complete POVM (SIC-POVM). Detectorfidelity is further improved through a composite error mitigation strategy thatincorporates twirling and a newly devised conditional readout error mitigation.Looking forward, we expect improvements in approximate compilation and hardwarenoise for dynamic circuits to enable generalized measurements of largermulti-qubit POVMs on superconducting qubits.

High-fidelity, multi-qubit generalized measurements with dynamic circuits