# Measuring complex partition function zeroes of Ising models in quantum simulators

## TL;DR

This paper proposes quantum simulation protocols to measure complex partition function zeroes of classical Ising models, providing insights into critical phenomena and phase transitions in many-body systems.

## Contribution

It introduces experimentally feasible protocols using simple quantum gates and measurements to locate partition function zeroes in quantum simulators, bridging theory and practical implementation.

## Key findings

- Numerical simulations demonstrate protocol effectiveness.
- Analysis of projection noise effects.
- Feasibility on current quantum platforms.

## Abstract

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.