Simulating String-Net States and Anyons on a Digital Quantum Computer

Finding physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties. In this talk I will focus on our proposal for realization of a large class of topologically ordered states and simulating their quasiparticle excitations on a digital quantum computer. To achieve this, we design a set of linear-depth quantum circuits to generate ground states of general string-net models together with unitary open-string operators to simulate the creation and braiding of Abelian and non-Abelian anyons. We show that while Abelian unitary string operators can be implemented with a constant depth quantum circuit, their non-Abelian counteparts require only a linear depth circuit. Our proposed scheme allows us to directly probe characteristic topological properties such as the braiding statistics and fusion channels of anyons.