Variational Quantum Simulation of Anyonic Chains

Abstract

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~$L_R\lceil\ln_2 p\rceil$ qubits, where~$\lceil x\rceil$ is the smallest integer~$\geq x$. The scheme is benchmarked by realizing the ground states of RSOS Hamiltonians in the~$A_p$ family for~$4\leq p\leq8$ 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~$\lceil\ln_2 p\rceil$ 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.