Exact solutions for the time-evolution of quantum spin systems under arbitrary waveforms using algebraic graph theory

• URL: http://arxiv.org/abs/2205.05195v1
• Date: Tue, 10 May 2022 22:34:13 GMT
• Title: Exact solutions for the time-evolution of quantum spin systems under arbitrary waveforms using algebraic graph theory
• Authors: Pierre-Louis Giscard and Mohammadali Foroozandeh
• Abstract summary: A general approach is presented that offers exact analytical solutions for the time-evolution of quantum spin systems during parametric waveforms of arbitrary functions of time. The proposed method consistently outperforms conventional numerical methods, including ODE and piecewise-constant propagator approximations.
• Score: 0.0966840768820136
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A general approach is presented that offers exact analytical solutions for the time-evolution of quantum spin systems during parametric waveforms of arbitrary functions of time. The proposed method utilises the \emph{path-sum} method that relies on the algebraic and combinatorial properties of walks on graphs. A full mathematical treatment of the proposed formalism is presented, accompanied by an implementation in \textsc{Matlab}. Using computation of the spin dynamics of monopartite, bipartite, and tripartite quantum spin systems under chirped pulses as exemplar parametric waveforms, it is demonstrated that the proposed method consistently outperforms conventional numerical methods, including ODE integrators and piecewise-constant propagator approximations.

Related papers

• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Numerical Methods for Quantum Spin Dynamics [0.0]
  This report is concerned with the efficiency of numerical methods for simulating quantum spin systems. The accuracy of existing techniques is assessed in the presence of chirped pulses. The results of this work are implemented in the Python package MagPy to provide a better error-to-cost ratio than current approaches.
  arXiv  Detail & Related papers  (2023-12-25T00:35:24Z)
• Quadratic Time-dependent Quantum Harmonic Oscillator [0.0]
  We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators. Our unitary-transformation-based approach provides a solution to our general quadratic time-dependent quantum harmonic model.
  arXiv  Detail & Related papers  (2022-11-23T19:50:49Z)
• Calculating non-linear response functions for multi-dimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion [68.8204255655161]
  We present a methodology for simulating multi-dimensional electronic spectra of molecular aggregates with coupling electronic excitation to a structured environment. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise.
  arXiv  Detail & Related papers  (2022-07-06T15:30:38Z)
• Variational Quantum Evolution Equation Solver [0.0]
  Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. We propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction-diffusion and the incompressible Navier-Stokes equations.
  arXiv  Detail & Related papers  (2022-04-06T16:02:11Z)
• Interaction of quantum systems with single pulses of quantized radiation [68.8204255655161]
  We describe the interaction of a propagating pulse of quantum radiation with a localized quantum system. By transformation to an appropriate picture, we identify the usual Jaynes-Cummings Hamiltonian between the scatterer and a superposition of the initial and final mode. The transformed master equation offers important insights into the system dynamics and it permits numerically efficient solutions.
  arXiv  Detail & Related papers  (2022-03-14T20:23:23Z)
• 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)
• Exact Floquet solutions of quantum driven systems [1.0152838128195467]
  We give out the exact Floquet solutions of wave function for three physical models. The idea presented in this paper can be used in mathematics to solve partial differential equations.
  arXiv  Detail & Related papers  (2022-02-02T15:15:05Z)
• Heisenberg treatment of multiphoton pulses in waveguide QED with time-delayed feedback [62.997667081978825]
  We propose a projection onto a complete set of states in the Hilbert space to decompose the multi-time correlations into single-time matrix elements. We consider the paradigmatic example of a two-level system that couples to a semi-infinite waveguide and interacts with quantum light pulses.
  arXiv  Detail & Related papers  (2021-11-04T12:29:25Z)
• Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model [0.0]
  We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment. Our framework can be used as a powerful and versatile tool for analyzing non-Markovian open system dynamics.
  arXiv  Detail & Related papers  (2021-08-12T13:49:22Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)

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.