Topological Quantum Computing on a Conventional Quantum Computer

Abstract

Majorana fermions are self-adjoint fermionic particles that are believed to exist as the elementary excitations in nanoengineered devices with superconductors and ferromagnets. They can be employed in topological quantum computation and can aid the solution of a class of spin models created by Kitaev. In both cases, the braiding of Majorana fermions plays a critical role in these applications. We explicitly construct quantum circuits for Majorana braiding and run them on IBM quantum computers to prepare the ground states of strongly correlated Kitaev-inspired models. The entanglement entropy for these models is then measured to determine quantum phase transitions. We show how maintaining particle-hole symmetry is critical to carrying out this work.