# Universal controlled-phase gate with cat-state qubits in circuit QED

## TL;DR

This paper proposes a simple, high-fidelity method to implement a universal controlled-phase gate between two cat-state qubits in circuit QED, utilizing a superconducting transmon qutrit to enhance coherence.

## Contribution

It introduces a novel gate scheme that operates with only two basic steps, avoiding classical pulses and measurements, applicable to microwave and optical resonators.

## Key findings

- Numerical simulations demonstrate high-fidelity gate performance.
- The method suppresses decoherence by keeping the qutrit in the ground state.
- The approach is compatible with current circuit QED technology.

## Abstract

Cat-state qubits (qubits encoded with cat states) have recently drawn intensive attention due to their enhanced life times with quantum error correction. We here propose a method to implement a universal controlled-phase gate of two cat-state qubits, via two microwave resonators coupled to a superconducting transmon qutrit. During the gate operation, the qutrit remains in the ground state; thus decoherence from the qutrit is greatly suppressed. This proposal requires only two basic operations and neither classical pulse nor measurement is needed; therefore the gate realization is simple. Numerical simulations show that high-fidelity implementation of this gate is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate with two microwave resonators or two optical cavities coupled to a single three-level natural or artificial atom.