Passive error correction with a qubit-oscillator system in noisy environment

TL;DR

This paper explores how a qubit-oscillator system with two-photon relaxation can be used to create a stable cat qubit that passively corrects errors by leveraging a superradiant phase transition and symmetry breaking.

Contribution

It demonstrates the formation of a passive error-correcting cat qubit in a dissipative qubit-oscillator system through symmetry-breaking phase transition.

Findings

Steady state exhibits superradiant phase transition.

Cat qubit can be stabilized in the steady state.

Passive error correction is effective against frequency fluctuations.

Abstract

In this paper, we study an open quantum system consisting of a qubit coupled to a harmonic oscillator subject to two-photon relaxation and demonstrate that such a system can be utilized to construct a cat qubit capable of passive error correction. To this end, we first show that the steady state of the qubit-oscillator system, described by the open quantum Rabi model with two-photon relaxation, undergoes a superradiant phase transition that breaks the strong symmetry of the Lindblad master equation. In the strong symmetry-broken phase, we show that a cat qubit can be stabilized in the steady state by tuning the qubit-oscillator coupling strength and demonstrate that passive error correction can be realized against errors due to fluctuations in the system frequencies. Our study deepens the understanding of dissipative phases in a qubit-oscillator system with strong symmetry and paves the way to utilize them for passive error correction.