Deformed Fredkin model for the $\nu{=}5/2$ Moore-Read state on thin cylinders

TL;DR

This paper introduces a simplified one-dimensional qubit model with deformed Fredkin gates that closely approximates the Moore-Read quantum Hall state on thin cylinders, enabling efficient quantum simulation and capturing key physical properties.

Contribution

The authors develop a new effective model using deformed Fredkin gates that simplifies the Moore-Read state on thin cylinders and demonstrates its accuracy and simulability.

Findings

High overlap between the Fredkin model ground state and Moore-Read wave function

Accurate reproduction of entanglement properties

Effective simulation of quench dynamics matching field theory predictions

Abstract

We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences $\lesssim 7$ magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a simpler one-dimensional chain of qubits with deformed Fredkin gates. We show that the ground state of the Fredkin model has high overlap with the Moore-Read wave function and accurately reproduces the latter's entanglement properties. Moreover, we demonstrate that the model captures the dynamical response of the Moore-Read state to a geometric quench, induced by suddenly changing the anisotropy of the system. We elucidate the underlying mechanism of the quench dynamics and show that it coincides with the linearized bimetric field theory. The minimal model introduced here can be directly implemented as a first step towards quantum simulation of the Moore-Read state, as we demonstrate by deriving an efficient circuit approximation to the ground state and implementing it on IBM quantum processor.