Quantum hardware has advanced to the point where it is now possible to perform simulations of physical systems and elucidate their topological and thermodynamic properties, which we will discuss in this talk. I will give a brief introduction to quantum computing and why they might be useful tools for solving problems in condensed matter physics and beyond. Following that, I will present a perspective on thermodynamics of quantum systems ideally suited to quantum computers, namely the zeros of the partition function, or Lee-Yang zeros. We developed quantum circuits to measure the Lee-Yang zeros, and used these to reconstruct the thermodynamic partition function of the XXZ model. The zeros qualitatively show the cross-over from an Ising-like regime to an XY-like regime, making this measurement ideally suitable in a NISQ environment. If time permits, I will discuss our demonstration of how topological properties of physical systems can be measured on quantum computers. We leverage the holonomy of the wavefunctions to obtain a noise-free measurement of the Chern number, which we apply to an interacting fermion model.