[RBRC seminar] Examining topology and thermodynamics using quantum computers
by
Lex Kemper
→
US/Eastern
Description
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. We 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 develop a quantum circuit to measure the Lee-Yang zeros, and use 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. Next, we demonstrate how topological properties of physical systems can be measured on quantum computers. When applied to the Kitaev spin model, we show that the identification of a topological phase transition is possible for an 8-qubit calculation on NISQ hardware. A second approach is to leverage the holonomy of the wavefunctions to obtain a noise-free measurement of the Chern number, which we apply to an interacting fermion model.
