  Interacting quantum systems illustrate complex phenomena including phase
transitions to novel ordered phases. The universal nature of critical phenomena
reduces their description to determining only the transition temperature and
the critical exponents. Numerically calculating these results for systems in
new universality classes is complicated due to critical slowing down, requiring
increasing resources near the critical point. An alternative approach
analytically continues the calculation onto the complex plane and determines
the partition function via its zeros. Here we show how to robustly perform this
analysis on noisy intermediate scale trapped ion quantum computers in a
scalable manner, using the XXZ model as a prototype. We illustrate the
transition from XY-like behavior to Ising-like behavior as a function of the
anisotropy. While quantum computers cannot yet scale to the thermodynamic
limit, our work provides a pathway to do so as hardware improves, allowing the
determination of critical phenomena for systems that cannot be solved
otherwise.
