Quantum covariant derivative

• URL: http://arxiv.org/abs/2206.01716v4
• Date: Sun, 19 Mar 2023 15:23:29 GMT
• Title: Quantum covariant derivative
• Authors: Ryan Requist
• Abstract summary: The quantum covariant derivative is used to derive a gauge- and coordinate-invariant adiabatic theory. It is proved to be covariant under gauge and coordinate transformations and compatible with the quantum geometric tensor.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate transformations and compatible with the quantum geometric tensor. The quantum covariant derivative is used to derive a gauge- and coordinate-invariant adiabatic perturbation theory, providing an efficient tool for calculations of nonlinear adiabatic response properties.

Related papers

• The multi-state geometry of shift current and polarization [44.99833362998488]
  We employ quantum state projectors to develop an explicitly gauge-invariant formalism. We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization. We reveal its decomposition into the sum of the skewness of the occupied states and intrinsic multi-state geometry.
  arXiv  Detail & Related papers  (2024-09-24T18:00:02Z)
• Geodesic nature and quantization of shift vector [3.998284861927654]
  We present the geodesic nature and quantization of geometric shift vector in quantum systems. Our analysis extends to include bosonic phonon drag shift vectors with non-vertical transitions. We reveal intricate relationships among geometric quantities such as the shift vector, Berry curvature, and quantum metric.
  arXiv  Detail & Related papers  (2024-05-22T05:18:52Z)
• Symmetric derivatives of parametrized quantum circuits [0.0]
  We introduce the concept of projected derivatives of parametrized quantum circuits. We show that the covariant derivative gives rise to the quantum Fisher information and quantum natural gradient.
  arXiv  Detail & Related papers  (2023-12-11T19:00:00Z)
• 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)
• Generalized quantum geometric tensor for excited states using the path integral approach [0.0]
  The quantum geometric tensor encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states. We then generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates.
  arXiv  Detail & Related papers  (2023-05-19T08:50:46Z)
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers [62.997667081978825]
  Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. We show that the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways even in small-scale non-Hermitian networks.
  arXiv  Detail & Related papers  (2023-02-23T09:43:49Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• A source fragmentation approach to interacting quantum field theory [0.0]
  We prove that the time-ordered Vacuum Expectation Values and the S-matrix of a regularized Lagrangian quantum theory can be approximated by a local operator. For the Wightman axioms, this suggests a modification that takes the algebra of measurement operators not to be generated by an operator-valued distribution.
  arXiv  Detail & Related papers  (2021-09-09T16:50:43Z)
• On quantum Hall effect: Covariant derivatives, Wilson lines, gauge potentials, lattice Weyl transforms, and Chern numbers [0.0]
  We show that the gauge symmetry of the nonequilibrium quantum transport of Chern insulator in a uniform electric field is governed by the Wilson line of parallel transport operator. This is dictated by the minimal coupling of derivatives with gauge fields in U (1) gauge theory.
  arXiv  Detail & Related papers  (2021-06-30T17:48:59Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)

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.