Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator

TL;DR

This paper introduces a Lindblad master equation that stabilizes finite-energy grid states in a quantum harmonic oscillator, demonstrating exponential convergence and potential for autonomous quantum error correction.

Contribution

It proposes a novel Lindblad dynamics based on stabilizer formalism that guarantees exponential stabilization of grid states for quantum error correction.

Findings

Exponential convergence rate established via Lyapunov function

Numerical simulations show robustness against photon-losses

Stabilization achieved for finite-energy grid states

Abstract

Based on the stabilizer formalism underlying Quantum Error Correction (QEC), the design of an original Lindblad master equation for the density operator of a quantum harmonic oscillator is proposed. This Lindblad dynamics stabilizes exactly the finite-energy grid states introduced in 2001 by Gottesman, Kitaev and Preskill for quantum computation. Stabilization results from an exponential Lyapunov function with an explicit lower-bound on the convergence rate. Numerical simulations indicate the potential interest of such autonomous QEC in presence of non-negligible photon-losses.