Deterministic preparation of GHZ entangled states with multiple superconducting qutrits in circuit QED

Abstract

Over the past decade, several works have been devoted to the generation of entangled states with superconducting (SC) qubits. Recently, attention has shifted to the generation of entangled states with SC qutrits (three-level quantum systems). However, the existing works are limited to the preparation of a maximally entangled EPR pair with two SC qutrits and a Greenberger-Horne-Zeilinger (GHZ) entangled state of three SC qutrits. We here propose a simple method to create a GHZ entangled state of multiple SC qutrits in circuit QED. The GHZ state is generated by employing multiple SC qutrits coupled to a microwave cavity or resonator. This proposal essentially operates by the cavity-qutrit dispersive interaction. By using this proposal, a GHZ state with an arbitrary number of SC qutrits can, in principle, be created. Since only a coupler cavity is utilized, the circuit hardware resources are minimized. No auxiliary energy levels of the qutrits are needed for the entangled state preparation. The GHZ state can be created deterministically. As an example, we analyze the experimental feasibility of preparing a GHZ state of five SC transmon qutrits within current circuit QED technology. This proposal is universal and can be extended to create a GHZ entangled state of multiple matter qutrits (e.g., atomic qutrits, quantum-dot qutrits, NV-center qutrits, Magnon qutrits, and various SC qutrits) by employing multiple natural or artificial three-level atoms coupled to a microwave or optical cavity.