Single Qubit State Estimation on NISQ Devices with Limited Resources and
  SIC-POVMs
Current quantum computers have the potential to overcome classical
computational methods, however, the capability of the algorithms that can be
executed on noisy intermediate-scale quantum devices is limited due to hardware
imperfections. Estimating the state of a qubit is often needed in different
quantum protocols, due to the lack of direct measurements. In this paper, we
consider the problem of estimating the quantum state of a qubit in a quantum
processing unit without conducting direct measurements of it. We consider a
parameterized measurement model to estimate the quantum state, represented as a
quantum circuit, which is optimized using the quantum tomographic transfer
function. We implement and test the circuit using the quantum computer of the
Technical Research Centre of Finland as well as an IBM quantum computer. We
demonstrate that the set of positive operator-valued measurements used for the
estimation is symmetric and informationally complete. Moreover, the resources
needed for qubit estimation are reduced when direct measurements are allowed,
keeping the symmetric property of the measurements.
Cristian A. Galvis-Florez Daniel Reitzner Simo Särkkä