Partition functions are ubiquitous in physics: they are important in determining the thermodynamic properties of many-body systems, and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here we show how to find partition function zeros on noisy intermediate-scale trapped ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their 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 future calculation of critical phenomena for systems beyond classical computing limits.

The experimental raw-data is obtained from trapped ion quantum computer. Data after post-selection to this raw-data is also used. Other data is from computer simulations.