  Studying the zeroes of partition functions in the space of complex control
parameters allows to understand formally how critical behavior of a many-body
system can arise in the thermodynamic limit despite various no-go theorems for
finite systems. In this work we propose protocols that can be realized in
quantum simulators to measure the location of complex partition function zeroes
of classical Ising models. The protocols are solely based on the implementation
of simple two-qubit gates, local spin rotations, and projective measurements
along two orthogonal quantization axes. Besides presenting numerical
simulations of the measurement outcomes for an exemplary classical model, we
discuss the effect of projection noise and the feasibility of the
implementation on state of the art platforms for quantum simulation.
