Stability and decoherence rates of a GKP qubit protected by dissipation

• URL: http://arxiv.org/abs/2304.03806v1
• Date: Fri, 7 Apr 2023 18:21:27 GMT
• Title: Stability and decoherence rates of a GKP qubit protected by dissipation
• Abstract summary: We give explicit upper bounds for the energy of the solutions of the Lindblad master equation. We show that the evolution of the Bloch sphere coordinates of a logical qubit is exponentially slow even in presence of small diffusive noise processes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator. It approximately stabilizes finite-energy periodic grid states called Gottesman-Kitaev-Preskill (GKP) states, that can be used to encode and protect a logical qubit. We give explicit upper bounds for the energy of the solutions of the Lindblad master equation. Using three periodic observables to define the Bloch sphere coordinates of a logical qubit, we show that their dynamics is governed by a diffusion partial differential equation on a 2D-torus with a Witten Laplacian. We show that the evolution of these logical coordinates is exponentially slow even in presence of small diffusive noise processes along the two quadratures of the phase space. Numerical simulations indicate similar results for other physically relevant noise processes.

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