Non-Stationary Long-Term Dynamics via Selected Incomplete Dual Bases
- URL: http://arxiv.org/abs/2306.07407v2
- Date: Tue, 22 Oct 2024 17:00:36 GMT
- Title: Non-Stationary Long-Term Dynamics via Selected Incomplete Dual Bases
- Authors: Hsiao-Han Chuang, Abhijit Pendse,
- Abstract summary: We propose an SU(2) coherent state basis and deriving equations of motion for both time-independent and time-dependent Hamiltonian.
We evaluate this method through numerical simulations of a seven-qubit system.
Our conclusion suggests that the selected incomplete dual basis method can efficiently capture both short-term and long-term dynamics.
- Score: 0.0
- License:
- Abstract: Simulating the dynamics of non-stationary, long-term many-body quantum systems poses significant challenges due to the large size of the state space. We are examining how traditional basis sets struggle to accurately represent long-term dynamics when using incomplete sets. To address this issue, we propose using an SU(2) coherent state basis and deriving equations of motion for both time-independent and time-dependent Hamiltonian. This methodology involves a sampling approach, where a subset of relevant configurations is chosen based on energy criteria, and a projection method is used to enhance the accuracy of wavefunction propagation while reducing computational cost. We evaluate this method through numerical simulations of a seven-qubit system, calculating key physical observables such as state probabilities and domain-wall densities. Our results indicate that while complete basis sets offer accurate dynamics, selected incomplete sets can recover essential features, especially with the assistance of a projector. Our conclusion suggests that the selected incomplete dual basis method can efficiently capture both short-term and long-term dynamics.
Related papers
- Photonic Simulation of Localization Phenomena Using Boson Sampling [0.0]
We propose boson sampling as an alternative compact synthetic platform performing at room temperature.
By mapping the time-evolution unitary of a Hamiltonian onto an interferometer via continuous-variable gate decompositions, we present proof-of-principle results of localization characteristics of a single particle.
arXiv Detail & Related papers (2024-10-17T18:00:05Z) - Truncated Gaussian basis approach for simulating many-body dynamics [0.0]
The approach constructs an effective Hamiltonian within a reduced subspace, spanned by fermionic Gaussian states, and diagonalizes it to obtain approximate eigenstates and eigenenergies.
Symmetries can be exploited to perform parallel computation, enabling to simulate systems with much larger sizes.
For quench dynamics we observe that time-evolving wave functions in the truncated subspace facilitates the simulation of long-time dynamics.
arXiv Detail & Related papers (2024-10-05T15:47:01Z) - 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) - Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment.
We find sufficient conditions under which dynamical decoupling works for such systems.
Our bounds reproduce the correct scaling in various relevant system parameters.
arXiv Detail & Related papers (2024-09-24T04:58:28Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - On optimization of coherent and incoherent controls for two-level
quantum systems [77.34726150561087]
This article considers some control problems for closed and open two-level quantum systems.
The closed system's dynamics is governed by the Schr"odinger equation with coherent control.
The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
arXiv Detail & Related papers (2022-05-05T09:08:03Z) - 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) - Realistic simulations of spin squeezing and cooperative coupling effects
in large ensembles of interacting two-level systems [0.0]
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay.
This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.
arXiv Detail & Related papers (2021-04-30T18:00:00Z) - 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) - Probing the topological Anderson transition with quantum walks [48.7576911714538]
We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters.
The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition.
arXiv Detail & Related papers (2021-02-01T21:19:15Z) - Quantum relaxation in a system of harmonic oscillators with
time-dependent coupling [0.0]
We analyze the relaxation of nonequilibrium initial distributions for a system of coupled one-dimensional harmonic oscillators.
We show that in general the system studied here tends to equilibrium, but the relaxation can be retarded depending on the values of the parameters.
arXiv Detail & Related papers (2020-07-06T12:57:18Z)
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.