Liouvillian Exceptional Points of Non-Hermitian Systems via Quantum
  Process Tomography
Hamiltonian exceptional points (HEPs) are spectral degeneracies of
non-Hermitian Hamiltonians describing classical and semiclassical open systems
with gain and/or loss. However, this definition overlooks the occurrence of
quantum jumps in the evolution of open quantum systems. These quantum effects
are properly accounted for by considering Liouvillians and their exceptional
points (LEPs) [Minganti et al., Phys. Rev. A {\bf 100}, 062131 (2019)]. Here,
we explicitly describe how standard quantum process tomography, which reveals
the dynamics of a quantum system, can be readily applied to reveal and
characterize LEPs of non-Hermitian systems. We conducted experiments on an IBM
quantum processor to implement a prototype model simulating the decay of a
single qubit through three competing channels. Subsequently, we performed
tomographic reconstruction of the corresponding experimental Liouvillians and
their LEPs using both single- and two-qubit operations. This example
underscores the efficacy of process tomography in tuning and observing LEPs,
despite the absence of HEPs in the model.
Shilan Abo Patrycja Tulewicz Karol Bartkiewicz Şahin K. Özdemir Adam Miranowicz