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
- Authors: Lev-Arcady Sellem, R\'emi Robin, Philippe Campagne-Ibarcq and Pierre
Rouchon
- 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.
Related papers
- KPZ scaling from the Krylov space [83.88591755871734]
Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported.
Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
arXiv Detail & Related papers (2024-06-04T20:57:59Z) - Radiative transport in a periodic structure with band crossings [52.24960876753079]
We derive the semi-classical model for the Schr"odinger equation in arbitrary spatial dimensions.
We consider both deterministic and random scenarios.
As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.
arXiv Detail & Related papers (2024-02-09T23:34:32Z) - Hilbert Space Fragmentation in Open Quantum Systems [0.7412445894287709]
We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems.
We find that it can stabilize highly entangled steady states.
arXiv Detail & Related papers (2023-05-05T18:00:06Z) - Survey of the Hierarchical Equations of Motion in Tensor-Train format
for non-Markovian quantum dynamics [0.0]
This work is a survey about the hierarchical equations of motion and their implementation with the tensor-train format.
We recall the link with the perturbative second order time convolution equations also known as the Bloch-Redfield equations.
The main points of the tensor-train expansion are illustrated in an example with a qubit interacting with a bath described by a Lorentzian spectral density.
arXiv Detail & Related papers (2023-03-08T14:21:43Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - Dynamical transitions from slow to fast relaxation in random open
quantum systems [0.0]
We study a model in which the system Hamiltonian and its couplings to the noise are random matrices whose entries decay as power laws of distance.
The steady state is always featureless, but the rate at which it is approached exhibits three phases depending on $alpha_H$ and $alpha_L$.
Within perturbation theory, the phase boundaries in the $(alpha_H, alpha_L)$ plane differ for weak and strong dissipation, suggesting phase transitions as a function of noise strength.
arXiv Detail & Related papers (2022-11-23T20:56:46Z) - Local Neumann semitransparent layers: resummation, pair production and
duality [0.0]
We consider local semitransparent Neumann boundary conditions for a quantum scalar field.
We interpret the effective action as a theory in a first-quantized phase space.
We prove the existence of a strong/weak duality that links this Neumann field theory to the analogue Dirichlet one.
arXiv Detail & Related papers (2022-08-15T18:00:18Z) - Dynamics of Fluctuations in Quantum Simple Exclusion Processes [0.0]
We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions.
We show that fluctuations of the fermionic degrees of freedom obey evolution equations of Lindblad type, and derive the corresponding Lindbladians.
We carry out a detailed analysis of the steady states and slow modes that govern the late time behaviour and show that the dynamics of fluctuations of observables is described in terms of closed sets of coupled linear differential-difference equations.
arXiv Detail & Related papers (2021-07-06T15:02:58Z) - Assessment of weak-coupling approximations on a driven two-level system
under dissipation [58.720142291102135]
We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation.
We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
arXiv Detail & Related papers (2020-11-11T22:45:57Z) - Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit.
We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront.
The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
arXiv Detail & Related papers (2020-03-09T21:27:02Z) - Einselection from incompatible decoherence channels [62.997667081978825]
We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators.
We show that Fock states remain the most robust states to decoherence up to a critical coupling.
arXiv Detail & Related papers (2020-01-29T14:15:19Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.