In this lecture, the speaker will present methods and algorithms for solving statistical mechanics problems, combinatorial optimization problems, and quantum circuit simulations, in an integrated framework based on tensor networks. In statistical mechanics problems, the partition function (i.e. the normalization factor of the Boltzmann distribution) at a finite temperature can be obtained by contracting a tensor network that is converted from the statistical mechanics problem. When equipped with the “Tropical” algebra, the tensor network contraction can be used to obtain ground state energy and entropy of the model directly at zero temperature. When the interactions in the statistical mechanics model are complex, computing the partition function acts as estimating the amplitude of an end state of a quantum circuit, thus tensor network contractions can be used to simulate quantum circuits. The speaker will introduce approximate and exact algorithms for contracting tensor networks, and their wide applications, particularly in simulating Google’s Sycamore quantum circuits.
About the speaker
Prof. Zhang Pan received his PhD on Theoretical Physics from Lanzhou University in 2009. He then worked as a Postdoctoral Research Fellow at the Politecnico di Torino (2009-2012), the ESPCI Paris (2012-2013) and the Santa Fe Institute (2013-2015). In 2015, he joined the Institute of Theoretical Physics, Chinese Academy of Sciences and is currently a Professor there.
Prof. Zhang’s research is in the interdisciplinary field between statistical physics, applied mathematics and computer science. He is also interested in spin glass theory and message passing algorithms, combinatorial optimization problems, random matrix theory, statistical inference, networks and machine learning problems.