  We demonstrate that genuinely non-Hermitian topological phases and
corresponding topological phase transitions can be naturally realized in
monitored quantum circuits, exemplified by the paradigmatic non-Hermitian
Su-Schrieffer-Heeger model. We emulate this model by a 1D chain of spinless
electrons evolving under unitary dynamics and subject to periodic measurements
that are stochastically invoked. The non-Hermitian topology is visible in
topological invariants adapted to the context of monitored circuits. For
instance, the topological phase diagram of the monitored realization of the
non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal
polarization computed from an effective Hamiltonian of the monitored system.
Importantly, our monitored circuit realization allows direct access to steady
state biorthogonal expectation values of generic observables, and hence, to
measure physical properties of a genuine non-Hermitian model. We expect our
results to be applicable more generally to a wide range of models that host
non-Hermitian topological phases.
