Hybrid Schrödinger-Liouville and projective dynamics

• URL: http://arxiv.org/abs/2504.05532v2
• Date: Sun, 20 Apr 2025 16:29:48 GMT
• Title: Hybrid Schrödinger-Liouville and projective dynamics
• Authors: Kaja Krhac, Frederic P. Schuller, Stefano Stramigioli,
• Abstract summary: We show how this alternatingly continuous and projective evolution can be cast in form of one single differential equation for a refined state space manifold.<n>We show how this alternatingly continuous and projective evolution can be cast in form of one single differential equation for a refined state space manifold.
• Score: 4.595636071139437
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum dynamics provides the arguably most fundamental example of hybrid dynamics: As long as no measurement takes place, the system state is governed by the Schr\"odinger-Liouville differential equation, which is however interrupted and replaced by projective dynamics at times when measurements take place. We show how this alternatingly continuous and projective evolution can be cast in form of one single differential equation for a refined state space manifold and thus be made amenable to standard port-theoretic analysis and control techniques.

Related papers

• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Unitary description of the Jaynes-Cummings model under fractional-time dynamics [0.0]
  We show that a unitary evolution can be achieved for a traceless two-level Hamiltonian.<n>We take into account the fractional-order parameter $alpha$ and its effect in unitary quantum dynamics.
  arXiv  Detail & Related papers  (2024-09-09T17:44:31Z)
• Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation [33.76659022113328]
  This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions.<n>We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions.<n>We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension.
  arXiv  Detail & Related papers  (2024-07-22T03:52:14Z)
• Variational quantum simulation using non-Gaussian continuous-variable systems [39.58317527488534]
  We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
  arXiv  Detail & Related papers  (2023-10-24T15:20:07Z)
• Effective nonlinear Ehrenfest hybrid quantum-classical dynamics [0.0]
  We analyze the case of Ehrenfest dynamics on systems defined by a probability density. We identify the relations of the non-linearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment.
  arXiv  Detail & Related papers  (2023-08-28T09:25:36Z)
• Quantum-jump vs stochastic Schr\"{o}dinger dynamics for Gaussian states with quadratic Hamiltonians and linear Lindbladians [0.0]
  We consider quantum-jump and Schr"odinger dynamics for initially Gaussian states. While both unravellings converge to the same Lindblad dynamics when averaged, the individual dynamics can differ qualitatively.
  arXiv  Detail & Related papers  (2022-03-22T08:13:10Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Engineering Dissipative Quasicrystals [7.182858821473896]
  We discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes. Our work suggests a systematic route toward engineering exotic quantum dynamics in open systems, based on insights of non-Hermitian physics.
  arXiv  Detail & Related papers  (2021-11-29T10:35:34Z)
• 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)
• Postselection-free entanglement dynamics via spacetime duality [0.0]
  The dynamics of entanglement in hybrid' non-unitary circuits has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply emphpostselection on random measurement outcomes. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of emphspacetime duality
  arXiv  Detail & Related papers  (2020-10-29T18:00:01Z)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)

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.