Variational Quantum Simulation of Anyonic Chains

Anyonic chains provide lattice realizations of a rich set of quantum field theories in two space-time dimensions. The latter play a central role in the investigation of generalized symmetries, renormalization group flows and numerous exotic phases of strongly-correlated systems. Here, a variational quantum simulation scheme is presented for the analysis of those anyonic chains which can be mapped to the restricted solid-on-solid (RSOS) models of Andrews, Baxter and Forrester. An L_R site RSOS model associated with a Dynkin diagram containing p nodes is realized with L_Rlceilln2 prceil qubits, where lceil xrceil is the smallest integer geq x. The scheme is benchmarked by realizing the ground states of RSOS Hamiltonians in the A_p family for 4leq pleq8 using a variational quantum-classical algorithm. The latter is based on the Euler-Cartan circuit ansatz. Topological symmetry operators are analyzed for the RSOS models at the quantum-critical points. Measurement of observables acting on lceilln₂ prceil qubits is shown to capture the anyonic nature of the Hilbert space. The described quantum simulation scheme provides a systematic approach to give rise to a large family of quantum field theories which have largely eluded physical realizations.