IF invites you to the No.7 IF Colloquium (Online Seminar Series)
Title: ” Complexity of approximating quantum many-body physics in thermal equilibrium “ Speaker: Anirban Narayan Chowdhury,Ph.D. , Institute for Quantum Computing (IQC), University of Waterloo, Canada—————————————-
Anirban received his PhD degree from Center for Quantum Information and Control (CQuIC), University of New Mexico, under the supervision of Rolando Somma from Los Alamos National Laboratory. He is currently a postdoctoral fellow at Institute for Quantum Computing (IQC), Waterloo, working at the intersection of quantum algorithms and many-body physics.
Abstract:The physical properties of a quantum many-body system in thermal equilibrium are determined by its partition function and free energy. Despite their fundamental importance , surprisingly little is known about the problem of approximating these quantities. In this talk, I will present some results from arxiv:2110.15466 where we study this problem for local qubit Hamiltonians.
Firstly, I will show that the problem of approximating partition functions is equivalent to three other fundamental problems including a natural quantum analogue of the well-known approximate counting task from classical computer science. I will also show that the task of approximating thermal expectation values of local observables is equivalent in computational complexity to approximating the partition function.
Finally, I will present a new efficient approximation algorithm for the free energy in the special case of dense Hamiltonians such as quantum many-body systems with all-to-all interactions. This algorithm is based on the variational characterization of the free energy: the main idea is to solve a “relaxed” convex optimization program over sets of reduced density matrices and then show that this in fact gives a good approximation to the free energy.
Keywords: Many-Body Physics, Quantum Computing, Thermal Equilibrium, Complexity Facebook Live Event : https://fb.me/e/61GrNjc5i IF Channel :
