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Conference Papers Year : 2022

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

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.

Dates and versions

hal-03627196 , version 1 (01-04-2022)

Identifiers

Cite

Lev-Arcady Sellem, Philippe Campagne-Ibarcq, Mazyar Mirrahimi, Alain Sarlette, Pierre Rouchon. Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator. 2022 IEEE 61st Conference on Decision and Control (CDC), Dec 2022, Cancun, Mexico. pp.5149-5154, ⟨10.1109/CDC51059.2022.9992722⟩. ⟨hal-03627196⟩
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