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

• URL: http://arxiv.org/abs/2203.16836v2
• Date: Thu, 8 Sep 2022 09:52:27 GMT
• Title: Exponential convergence of a dissipative quantum system towards finite-energy grid states of an oscillator
• Authors: Lev-Arcady Sellem, Philippe Campagne-Ibarcq, Mazyar Mirrahimi, Alain Sarlette, Pierre Rouchon
• Abstract summary: Lindblad dynamics stabilizes exactly the finite-energy grid states introduced in 2001 by Gottesman, Kitaev and Preskill for quantum computation. Numerical simulations indicate the potential interest of such autonomous QEC in presence of non-negligible photon-losses.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Megastable quantization in self-excited systems [0.0]
  A classical particle in a confining potential gives rise to a Hamiltonian conservative dynamical system. The corresponding quantum particle exhibits countably infinite discrete energy levels. Our formalism can be extended to self-excited particles in general confining potentials.
  arXiv  Detail & Related papers  (2024-06-06T09:40:57Z)
• Hysteresis and Self-Oscillations in an Artificial Memristive Quantum Neuron [79.16635054977068]
  We study an artificial neuron circuit containing a quantum memristor in the presence of relaxation and dephasing. We demonstrate that this physical principle enables hysteretic behavior of the current-voltage characteristics of the quantum device.
  arXiv  Detail & Related papers  (2024-05-01T16:47:23Z)
• Kibble-Zurek mechanism and errors of gapped quantum phases [0.25602836891933073]
  Kibble-Zurek mechanism relates the domain of non-equilibrium dynamics with the critical properties at equilibrium. We present a novel numerical scheme to estimate the scaling exponent wherein the notion of defects is mapped to errors.
  arXiv  Detail & Related papers  (2024-01-24T17:57:27Z)
• Emergent equilibrium and quantum criticality in a two-photon dissipative oscillator [0.0]
  We study the dissipative phase transition in a quantum oscillator with two-photon drive and two-photon dissipation. We construct a theory of non-perturbative quantum fluctuations and go beyond the semi-classical approximation. We provide a description of the quantum critical region and obtain critical exponents that appear to be in very good agreement with numerical simulations.
  arXiv  Detail & Related papers  (2023-11-01T05:03:44Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps [0.0]
  We implement a quantum state trajectory scheme for solving Lindblad quantum master equations. We show the potential for solving the dissipative dynamics of finite size arrays of strongly interacting quantized oscillators with high excitation densities.
  arXiv  Detail & Related papers  (2022-08-02T03:01:14Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Lyapunov-Based Stabilization and Control of Closed Quantum Systems [0.36748639131154304]
  The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite operator in the Lyapunov function provides additional degrees of freedom for the designer.
  arXiv  Detail & Related papers  (2021-01-31T00:20:58Z)
• Signatures of Liouvillian exceptional points in a quantum thermal machine [20.83362404425491]
  We characterize a quantum thermal machine as a non-Hermitian quantum system. We show that the thermal machine features a number of Liouvillian exceptional points (EPs) for experimentally realistic parameters.
  arXiv  Detail & Related papers  (2021-01-27T17:19:35Z)
• Entanglement robustness to excitonic spin precession in a quantum dot [43.55994393060723]
  A semiconductor quantum dot (QD) is an attractive resource to generate polarization-entangled photon pairs. We study the excitonic spin precession (flip-flop) in a family of QDs with different excitonic fine-structure splitting (FSS) Our results reveal that coherent processes leave the time post-selected entanglement of QDs unaffected while changing the eigenstates of the system.
  arXiv  Detail & Related papers  (2020-01-31T13:50:51Z)

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.