Simulation of positive operator-valued measures and quantum instruments
  via quantum state preparation algorithms
In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm
to implement, in a circuit-based quantum computer, a general quantum
measurement (GQM) of a two-level quantum system, a qubit. Even though their
algorithm seems right, its application involves the solution of an intricate
non-linear system of equations in order to obtain the angles determining the
quantum circuit to be implemented for the simulation. In this article, we
identify and discuss a simple way to circumvent this issue and implement GQMs
on any $d$-level quantum system through quantum state preparation algorithms.
Using some examples for one qubit, one qutrit and two qubits, we illustrate the
easy of application of our protocol. Besides, we show how one can utilize our
protocol for simulating quantum instruments, for which we also give an example.
All our examples are demonstrated using IBM's quantum processors.
Douglas F. Pinto Marcelo S. Zanetti Marcos L. W. Basso Jonas Maziero