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Interacting quantum systems illustrate complex phenomena including phasetransitions to novel ordered phases. The universal nature of critical phenomenareduces their description to determining only the transition temperature andthe critical exponents. Numerically calculating these results for systems innew universality classes is complicated due to critical slowing down, requiringincreasing resources near the critical point. An alternative approachanalytically continues the calculation onto the complex plane and determinesthe partition function via its zeros. Here we show how to robustly perform thisanalysis on noisy intermediate scale trapped ion quantum computers in ascalable manner, using the XXZ model as a prototype. We illustrate thetransition from XY-like behavior to Ising-like behavior as a function of theanisotropy. While quantum computers cannot yet scale to the thermodynamiclimit, our work provides a pathway to do so as hardware improves, allowing thedetermination of critical phenomena for systems that cannot be solvedotherwise.

Many Body Thermodynamics on Quantum Computers via Partition Function Zeros