Variational quantum simulation of interacting electrons and interacting non-Abelian anyons
Recent advances in quantum computing technologies have made it possible to create controlled quantum states remotely, “in the cloud.” Although current processors still face significant limitations in terms of scale and noise levels, hybrid quantum-classical algorithms, combined with error mitigation techniques on pre-fault-tolerant processors, are yielding impressive results that may soon surpass the best obtainable outcomes from classical (super)computers. At the core of these effective hybrid algorithms are efficient quantum circuit ansatzes.
In my talk, I will focus on constructing efficient quantum circuits and the variational quantum eigensolver (VQE) algorithm, with applications in quantum chemistry/material science and topological quantum physics. Specifically, for quantum chemistry, I will demonstrate the construction of particle-conserving brick-wall quantum circuits and the setup of the VQE algorithm to calculate low-energy states, supported by simulation results of the Heisenberg XXZ model. For topological quantum physics, I will illustrate how to build circuits that mathematically model non-Abelian anyons on qubit gate-based processors, including the simulation results of interacting Fibonacci anyons.