Energy preserving evolutions over Bosonic systems

• URL: http://arxiv.org/abs/2307.13801v4
• Date: Mon, 02 Dec 2024 21:18:31 GMT
• Title: Energy preserving evolutions over Bosonic systems
• Authors: Paul Gondolf, Tim Möbus, Cambyse Rouzé,
• Abstract summary: We investigate perturbations of quantum dynamical semigroups that operate on continuous variable systems. We provide a new scheme for deriving continuity bounds on the energy-constrained capacities of Markovian perturbations of quantum dynamical semigroups.
• Score: 1.7478203318226315
• License:
• Abstract: The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to the code-space - an invariant subspace protected against certain types of errors. In this paper, we investigate perturbations of quantum dynamical semigroups that operate on continuous variable (CV) systems and admit an invariant subspace. First, we prove a generation theorem for quantum Markov semigroups on CV systems under the physical assumptions that (i) the generator is in GKSL form with corresponding jump operators defined as polynomials of annihilation and creation operators; and (ii) the (possibly unbounded) generator increases all moments in a controlled manner. Additionally, we show that the level sets of operators with bounded first moments are admissible subspaces of the evolution, providing the foundations for a perturbative analysis. Our results also extend to time-dependent semigroups and multi-mode systems. We apply our general framework to two settings of interest in continuous variable quantum information processing. First, we provide a new scheme for deriving continuity bounds on the energy-constrained capacities of Markovian perturbations of quantum dynamical semigroups. Second, we provide quantitative perturbation bounds for the steady state of the quantum Ornstein-Uhlenbeck semigroup and the invariant subspace of the photon dissipation used in bosonic error correction.

Related papers

• Simulating continuous-space systems with quantum-classical wave functions [0.0]
  Non-relativistic interacting quantum many-body systems are naturally described in terms of continuous-space Hamiltonians. Current algorithms require discretization, which usually amounts to choosing a finite basis set, inevitably introducing errors. We propose an alternative, discretization-free approach that combines classical and quantum resources in a global variational ansatz.
  arXiv  Detail & Related papers  (2024-09-10T10:54:59Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Non-adiabatic holonomic quantum operations in continuous variable systems [2.4060220973816144]
  Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to its potential robustness. Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes.
  arXiv  Detail & Related papers  (2024-02-04T07:06:23Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
  Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit. Despite their promise, the trainability of these algorithms is hindered by barren plateaus. We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
  arXiv  Detail & Related papers  (2023-09-17T18:14:10Z)
• 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)
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches [0.0]
  We calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. Our analyses provide a deeper understanding on the role of quantum information quantities for the dynamics of emergent phenomena reminiscent to systems in high-energy physics.
  arXiv  Detail & Related papers  (2022-10-27T18:00:01Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.