Geodesic Quantum Walks

• URL: http://arxiv.org/abs/2202.10235v2
• Date: Tue, 22 Feb 2022 17:33:12 GMT
• Title: Geodesic Quantum Walks
• Authors: Giuseppe Di Molfetta and Victor Deng
• Abstract summary: We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. We extend and generalize the duality principle introduced by one of the authors, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker. We proved that in the formal continuous limit, in both space and time, this new family of quantum walks converges to the (1+2)D massless Dirac equation on curved manifolds. We believe that this result has relevance in both modelling/simulating quantum transport on discrete curved structures, such as fullerene molecules or dynamical causal triangulation, and in addressing fast and efficient optimization problems in the context of the curved space optimization methods.

Related papers

• Completeness Relation in Renormalized Quantum Systems [0.0]
  We show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the initial Hamiltonian, having a discrete spectrum, is modified by a delta potential. The formulation can be easily extended to $N$ center case, and the case where delta interaction is supported on curves in the plane or space.
  arXiv  Detail & Related papers  (2024-09-09T07:09:16Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Twisted quantum walks, generalised Dirac equation and Fermion doubling [0.0]
  We introduce a new family of quantum walks, said twisted, which admits as continuous limit, a generalized Dirac operator equipped with a dispersion term. This quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.
  arXiv  Detail & Related papers  (2022-12-28T15:22:16Z)
• Qubit Geodesics on the Bloch Sphere from Optimal-Speed Hamiltonian Evolutions [0.0]
  We present an explicit geodesic analysis of the trajectories that emerge from the quantum evolution of a single-qubit quantum state. In addition to viewing geodesics in ray space as paths of minimal length, we also verify the geodesicity of paths in terms of unit geometric efficiency and vanishing geometric phase.
  arXiv  Detail & Related papers  (2022-10-17T14:44:03Z)
• Manipulating Generalized Dirac Cones In Quantum Metasurfaces [68.8204255655161]
  We consider a collection of single quantum emitters arranged in a honeycomb lattice with subwavelength periodicity. We show that introducing uniaxial anisotropy in the lattice results in modified dispersion relations.
  arXiv  Detail & Related papers  (2022-03-21T17:59:58Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Lattice Renormalization of Quantum Simulations [8.771066413050963]
  We show that trotterized time-evolution operators can be related by analytic continuation to the Euclidean transfer matrix on an anisotropic lattice. Based on the tools of Euclidean lattice field theory, we propose two schemes to determine Minkowski lattice spacings.
  arXiv  Detail & Related papers  (2021-07-02T16:10:45Z)
• Evolution of confined quantum scalar fields in curved spacetime. Part II [0.0]
  We develop a method for computing the Bogoliubov transformation experienced by a confined quantum scalar field in a globally hyperbolic spacetime. We prove this utility by addressing two problems in the perturbative regime: Dynamical Casimir Effect and gravitational wave resonance.
  arXiv  Detail & Related papers  (2021-06-28T18:05:50Z)
• 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)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Hyperentanglement in structured quantum light [50.591267188664666]
  Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols. Here, we demonstrate a functional source of high-dimensional, noise-resilient hyperentangled states encoded in time-frequency and vector-vortex structured modes. We generate highly entangled photon pairs at telecom wavelength that we characterise via two-photon interference and quantum state tomography, achieving near-unity visibilities and fidelities.
  arXiv  Detail & Related papers  (2020-06-02T18:00:04Z)

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.