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arXiv · 2203.16836

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

Lev-Arcady Sellem·Philippe Campagne-Ibarcq·Mazyar Mirrahimi·Alain Sarlette·Pierre Rouchon
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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.

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Lev-Arcady Sellem, Philippe Campagne-Ibarcq, Mazyar Mirrahimi, Alain Sarlette, Pierre Rouchon. 2022-03-31. Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator. https://doi.org/10.1109/cdc51059.2022.9992722

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