Pretty Good State Transfer and Minimal Polynomials

• URL: http://arxiv.org/abs/2010.06779v1
• Date: Wed, 14 Oct 2020 02:24:20 GMT
• Title: Pretty Good State Transfer and Minimal Polynomials
• Authors: Christopher M. van Bommel
• Abstract summary: We provide cases where pretty good state transfer can be ruled out. We also provide new examples of simple, unweighted graphs exhibiting pretty good state transfer.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum state transfer in terms of minimal polynomials, and provide cases where pretty good state transfer can be ruled out. We also provide new examples of simple, unweighted graphs exhibiting pretty good state transfer. Finally, we consider modifying paths by adding symmetric weighted edges, and apply these results to this case.

Related papers

• Pretty good state transfer among large sets of vertices [0.0]
  In a continuous-time quantum walk on a network of qubits, pretty good state transfer is the phenomenon of state transfer between two vertices with fidelity arbitrarily close to 1. We construct families of graphs to demonstrate that there is no bound on the size of a set of vertices that admit pretty good state transfer between any two vertices of the set.
  arXiv  Detail & Related papers  (2023-05-23T17:24:14Z)
• Quantum walks on simplexes and multiple perfect state transfer [0.0]
  In this paper, we study quantum walks on the extension of association schemes. Since only few examples of multiple (perfect) state transfer are known, we aim to make some additions in this collection.
  arXiv  Detail & Related papers  (2022-10-24T10:46:40Z)
• The quantum commuting model (Ia): The CHSH game and other examples: Uniqueness of optimal states [91.3755431537592]
  We use the universal description of quantum commuting correlations as state space on the universal algebra for two player games. We find that the CHSH game leaves a single optimal state on this common algebra.
  arXiv  Detail & Related papers  (2022-10-07T17:38:31Z)
• 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)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• Constructing graphs having Laplacian pair state transfer by an edge perturbation [7.7566555097445455]
  We construct many new graphs having Laplacian perfect pair state transfer as well as Laplacian pretty good pair state transfer. By those sufficient conditions, we also construct many new graphs having Laplacian perfect pair state transfer as well as Laplacian pretty good pair state transfer.
  arXiv  Detail & Related papers  (2022-02-10T11:22:37Z)
• Pretty good state transfer in discrete-time quantum walks [0.0]
  We establish the theory for pretty good state transfer in discrete-time quantum walks. For a class of walks, we show that pretty good state transfer is characterized by the spectrum of certain Hermitian adjacency matrix of the graph.
  arXiv  Detail & Related papers  (2021-05-08T18:55:57Z)
• Counterexamples to the Low-Degree Conjecture [80.3668228845075]
  A conjecture of Hopkins posits that for certain high-dimensional hypothesis testing problems, no-time algorithm can outperform so-called "simple statistics" This conjecture formalizes the beliefs surrounding a line of recent work that seeks to understand statistical-versus-computational tradeoffs.
  arXiv  Detail & Related papers  (2020-04-17T21:08:11Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)
• Perfect State Transfer on Oriented Graphs [0.0]
  We study the phenomena, unique to oriented graphs, of multiple state transfer. We give a characterization of multiple state transfer, and a new example of a graph where it occurs.
  arXiv  Detail & Related papers  (2020-02-11T20:34:54Z)
• A refinement of Reznick's Positivstellensatz with applications to quantum information theory [72.8349503901712]
  In Hilbert's 17th problem Artin showed that any positive definite in several variables can be written as the quotient of two sums of squares. Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of the squared norm of the variables.
  arXiv  Detail & Related papers  (2019-09-04T11:46:26Z)

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.