Specifying the unitary evolution of a qudit for a general nonstationary Hamiltonian via the generalized Gell-Mann representation

• URL: http://arxiv.org/abs/2004.09896v1
• Date: Tue, 21 Apr 2020 10:49:19 GMT
• Title: Specifying the unitary evolution of a qudit for a general nonstationary Hamiltonian via the generalized Gell-Mann representation
• Authors: Elena R. Loubenets and Christian K\"ading
• Abstract summary: We introduce a new general formalism describing the unitary evolution of a qudit $(dgeq2)$ in terms of the Bloch-like vector space. We derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit $(d\geq2)$ in terms of the Bloch-like vector space and specify how in a general case this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case $(d=2)$, we specify the unitary evolution of a qubit via the evolution of a unit vector in $\mathbb{R}^{4}$ and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians. This new analytical expression includes the qubit solutions known in the literature only as particular cases.

Related papers

• Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
  We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
  arXiv  Detail & Related papers  (2024-10-31T14:36:38Z)
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
  We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-21T10:56:49Z)
• Jaynes-Cummings model in a unitary fractional-time description [0.0]
  We show that a unitary evolution can be achieved for a traceless two-level Hamiltonian. We apply the unitary description to the Jaynes-Cummings model in the fractional-time scenario.
  arXiv  Detail & Related papers  (2024-09-09T17:44:31Z)
• Some new considerations about the $ν$-function [0.0]
  We show that the $nu$-function plays the role of the normalization function of generalized hypergeometric coherent states for quantum systems with a continuous spectrum. To our knowledge, the results obtained by us do not appear in the literature.
  arXiv  Detail & Related papers  (2024-09-09T10:08:17Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Time evolution operator for a $\left\{ h(1) \oplus h(1) \right\} \uplus u(2)$ time-dependent quantum Hamiltonian; a self-consistent resolution method based on Feynman's disentangling rules [0.0]
  It is shown that all the problem reduces to solve a complex Riccati-type differential equation. Some closed solutions to this differential equation are found and then concrete disentangling expressions for the time-ordered evolution operator are given.
  arXiv  Detail & Related papers  (2023-06-25T12:47:11Z)
• Quantum-based solution of time-dependent complex Riccati equations [0.0]
  We show a time-dependent complex Riccati equation (TDCRE) as the solution of the time evolution operator (TEO) of quantum systems. The inherited symmetries of quantum systems can be recognized by a simple inspection of the TDCRE. As an application, but also as a consistency test, we compare our solution with the analytic one for the Bloch-Riccati equation.
  arXiv  Detail & Related papers  (2022-09-07T23:52:04Z)
• 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)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Recursive Generation of The Semi-Classical Expansion in Arbitrary Dimension [0.0]
  We present a procedure based on the small time expansion of the propagator. We generate a semi-classical expansion of the textitquantum action for a quantum mechanical potential in arbitrary dimensions.
  arXiv  Detail & Related papers  (2020-12-11T00:06:26Z)
• 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)

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.