Examples

Before looking at the examples, it is advised that you read the Getting Started Guide.

The examples described below can be accessed via HQStage.

1. spinful_fermions_groundstate.ipynb

   In this example, we show how to compute the ground state of the Hamiltonian of a many-particle system.

2. spin_waves.ipynb

   This example introduces spin systems and time evolution. We consider the time evolution of a Heisenberg spin model in an excited state.

3. nonequilibrium_electron_transport.ipynb

   This example simulates the time evolution of a system of electrons starting in a nonequilibrium state.

4. spinless_fermions_greens_function.ipynb

   Example for the Calculation of the Spectral function using HQS Quantum Solver and Lattice Functions.

   This method combines operators, Chebyshev expansion, cluster perturbation theory and clever Green's function mathematics to create the reciprocal-space resolved spectral function (a. k. a. the interacting band structure) in a honeycomb lattice causing an opening of the Dirac point.

5. spinful_fermions_greens_function.ipynb

   Prototype example for the Calculation of the Spectral function of the Hubbard model using HQS Quantum Solver. In this approach we represent the wavefunction as a dyadic product of up and down states.

   Similar to the previous example, this example computes the interacting band structure of a square lattice under the influence of interaction. We retrieve the expected behaviour of opening a gap at half-filling.

6. bose_hubbard_groundstate.ipynb

   In this example we compute the groundstates of Bose-Hubbard systems, which is a simple bosonic system.

7. lidar.ipynb

   In this scientific example we study properties of light emitted by multiple atoms, a fundamental model in quantum optics. We use the HQS Quantum Solver to time evolve the system according to the Lindblad equation of motion and calculate various expectation values of system operators describing properties of the emitted light.