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Current quantum computers have the potential to overcome classicalcomputational methods, however, the capability of the algorithms that can beexecuted on noisy intermediate-scale quantum devices is limited due to hardwareimperfections. Estimating the state of a qubit is often needed in differentquantum protocols, due to the lack of direct measurements. In this paper, weconsider the problem of estimating the quantum state of a qubit in a quantumprocessing unit without conducting direct measurements of it. We consider aparameterized measurement model to estimate the quantum state, represented as aquantum circuit, which is optimized using the quantum tomographic transferfunction. We implement and test the circuit using the quantum computer of theTechnical Research Centre of Finland as well as an IBM quantum computer. Wedemonstrate that the set of positive operator-valued measurements used for theestimation is symmetric and informationally complete. Moreover, the resourcesneeded for qubit estimation are reduced when direct measurements are allowed,keeping the symmetric property of the measurements.

Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs