Engineering three-body interaction and Pfaffian states in circuit QED systems

TL;DR

This paper proposes a method to engineer three-body interactions in circuit QED systems to realize Pfaffian states, which are relevant for topological quantum computing, using tunable fluxonium qubits and synthetic magnetic fields.

Contribution

It introduces a scheme to create three-body interactions and stabilize Pfaffian states in circuit QED lattices, advancing topological quantum simulation.

Findings

Successfully engineered three-body interactions in circuit QED.

Demonstrated stabilization of Pfaffian states with next-nearest neighbor tunneling.

Showed feasibility of implementation with current technology.

Abstract

We demonstrate a scheme to engineer the three-body interaction in circuit-QED systems by tuning a fluxonium qubit. Connecting such qubits in a square lattice and controlling the tunneling dynamics, in the form of a synthesized magnetic field, for the photon-like excitations of the system, allows the implementation of a parent Hamiltonian whose ground state is the Pfaffian wave function. Furthermore, we show that the addition of the next-nearest neighbor tunneling stabilizes the ground state, recovering the expected topological degeneracy even for small lattices. Finally, we discuss the implementation of these ideas with the current technology.