Towards a benchmark for quantum computers based on an iterated
  post-selective protocol
Applying post selection in each step of an iterated protocol leads to
sensitive quantum dynamics that may be utilized to test and benchmark current
quantum computers. An example of this type of protocols was originally proposed
for the task of matching an unknown quantum state to a reference state. We
propose to employ the quantum state matching protocol for the purpose of
testing and benchmarking quantum computers. In particular, we implement this
scheme on freely available IBM superconducting quantum computers. By comparing
measured values with the theoretical conditional probability of the single,
final post-selected qubit, which is easy to calculate classically, we define a
benchmark metric. Additionally, the standard deviation of the experimental
results from their average serves as a secondary benchmark metric,
characterizing fluctuations in the given device. A peculiar feature of the
considered protocol is that there is a phase parameter of the initially
prepared state, on which the resulting conditional probability should not
depend. A careful analysis of the measured values indicates that its dependence
on the initial phase can reveal useful information about coherent gate errors
of the quantum device.
Adrian Ortega Orsolya Kálmán Tamás Kiss