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Studying the zeroes of partition functions in the space of complex controlparameters allows to understand formally how critical behavior of a many-bodysystem can arise in the thermodynamic limit despite various no-go theorems forfinite systems. In this work we propose protocols that can be realized inquantum simulators to measure the location of complex partition function zeroesof classical Ising models. The protocols are solely based on the implementationof simple two-qubit gates, local spin rotations, and projective measurementsalong two orthogonal quantization axes. Besides presenting numericalsimulations of the measurement outcomes for an exemplary classical model, wediscuss the effect of projection noise and the feasibility of theimplementation on state of the art platforms for quantum simulation.

Measuring complex partition function zeroes of Ising models in quantum simulators