Partial and complete qubit estimation using a single observable:
  optimization and quantum simulation
Quantum state estimation is an important task of many quantum information
protocols. We consider two families of unitary evolution operators, one with a
one-parameter and the other with a two-parameter, which enable the estimation
of a single spin component and all spin components, respectively, of a
two-level quantum system. To evaluate the tomographic performance, we use the
quantum tomographic transfer function (qTTF), which is calculated as the
average over all pure states of the trace of the inverse of the Fisher
information matrix. Our goal is to optimize the qTTF for both estimation
models. We find that the minimum qTTF for the one-parameter model is achieved
when the entangling power of the corresponding unitary operator is at its
maximum. The models were implemented on an IBM quantum processing unit, and
while the estimation of a single-spin component was successful, the whole spin
estimation displayed relatively large errors due to the depth of the associated
circuit. To address this issue, we propose a new scalable circuit design that
improves qubit state tomography when run on an IBM quantum processing unit.
Cristian A. Galvis Florez J. Martínez-Cifuentes K. M. Fonseca-Romero