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Many-body thermodynamics on quantum computers via partition function zeros

TitleMany-body thermodynamics on quantum computers via partition function zeros
Publication TypeJournal Article
Year of Publication2021
AuthorsA. Francis, D. Zhu, C. Huerta Alderete, S. Johri, X. Xiao, J. K. Freericks, C. Monroe, N. M. Linke, and A. F. Kemper
JournalScience Advances
Keywordsquantum computing

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.