Abstract
In this talk I will introduce an on-going work on analyzing the mixing times of fermionic systems through the parent Hamiltonian approach. I will first review the current method for constructing parent Hamiltonians for qubit Lindbladians proposed by Chen, Kastoryano, and Gilyén. When directly applying this method to fermionic systems, we will see that it fails to preserve fermionic locality, and I will talk about how this can be fixed using the third quantization formalism invented by Prosen. This yields a quasi-local fermionic parent Hamiltonian. I will then discuss its implications on the mixing times, especially for fermionic systems with a small but constant interaction term on each site. In the end I will discuss open problems regarding the quantum advantage in this scenario, and possible approaches to address strongly interacting fermionic systems.