Effective dynamics of qubit networks via phase-covariant quantum ensembles

• URL: http://arxiv.org/abs/2404.15223v2
• Date: Thu, 03 Oct 2024 16:15:38 GMT
• Title: Effective dynamics of qubit networks via phase-covariant quantum ensembles
• Authors: Sean Prudhoe, Unnati Akhouri, Tommy Chin, Sarah Shandera,
• Abstract summary: We generate ensembles of phase-covariant maps associated to the individual spins of a closed quantum system. The construction procedure suggests new ways to realize random families of open-system dynamics.
• Score: 0.0
• License:
• Abstract: We derive a new constructive procedure to rapidly generate ensembles of phase-covariant dynamical maps that may be associated to the individual spins of a closed quantum system. We do this by first computing the single-spin dynamical maps in small XXZ networks and chains, specialized to the class of initial states that guarantees phase-covariant dynamics for each spin. Since the dynamics in any small, closed system contains oscillatory features associated to the system size, we define an averaging procedure to extract time-homogeneous dynamics. We use the the average map and the set of deviations from the average map in the exactly derived ensembles to motivate the form of distributional functions for map parameters. The distributions then straightforwardly generate arbitrary-sized ensembles of channels, constrained by a few global properties. This procedure can also generate ensembles where individual maps are not phase-covariant although the average map is, corresponding to realizations of disordered, or noisy, Hamiltonians. The construction procedure suggests new ways to realize random families of open-system dynamics, subject to constraints that require the ensemble to approximate a partition of a closed system.

Related papers

• Equivalence of dynamics of disordered quantum ensembles and semi-infinite lattices [44.99833362998488]
  We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice. This mapping provides a geometric interpretation on the loss of coherence when averaging over the ensemble and allows computation of the exact dynamics of the entire disordered ensemble in a single simulation.
  arXiv  Detail & Related papers  (2024-06-25T18:13:38Z)
• Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method [0.0]
  Nonequilibrium dynamics of highly-controlled quantum systems is a challenging issue in statistical physics. We develop a discrete phase-space approach for general SU($N$) spin systems that capture non-trivial quantum correlations inside each cluster. We demonstrate that the cluster discrete truncated Wigner approximation can reproduce key results in a recent experiment on the correlation propagation dynamics in a two dimensional Bose-Hubbard system.
  arXiv  Detail & Related papers  (2024-04-29T11:08:44Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Approximation of nearly-periodic symplectic maps via structure-preserving neural networks [0.3913403111891026]
  A continuous-time dynamical system with parameter $varepsilon$ is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as $varepsilon$ approaches 0. We construct a novel structure-preserving neural network to approximate nearly-periodic symplectic maps.
  arXiv  Detail & Related papers  (2022-10-11T01:59:47Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• Graph Gamma Process Generalized Linear Dynamical Systems [60.467040479276704]
  We introduce graph gamma process (GGP) linear dynamical systems to model real multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a parsimonious set of multivariate sub-sequences. We use the generated random graph, whose number of nonzero-degree nodes is finite, to define both the sparsity pattern and dimension of the latent state transition matrix.
  arXiv  Detail & Related papers  (2020-07-25T04:16:34Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Classical Models of Entanglement in Monitored Random Circuits [0.0]
  We show the evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements. We also establish a Markov model for the evolution of the zeroth R'enyi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-R'enyi-entropy model.
  arXiv  Detail & Related papers  (2020-04-14T18:00:14Z)

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.