Add Lanczos algorithm to Qiskit dynamics

[miamico]

Description

The Lanczos algorithm is a numerical method that can be used to calculate time-evolution of closed quantum system. It is a computationally efficient method for large systems and can be useful to speed up the simulation of closed-system dynamics.

Deliverables

PR to Qiskit dynamics repo to add the feature

Mentors details

• Mentor 1
  • Name: Mirko Amico
  • GitHub ID: @miamico
  • What they do: Qiskit Research

Number of mentees

1

Type of mentees

• Mentee 1
  • Required:
  • Good knowledge of linear algebra
  • Good knowledge of Python
  • Some knowledge of quantum systems dynamics
  • Nice to have:
  • Experience in numerical methods for quantum system dynamics

[rupeshknn]

Here is the pdf of the presentation: Checkpoint_1-Lanczos_Algorithm_for_Qiskit_Dynamics.pdf

[HuangJunye]

@rupeshknn Can you please provide your checkpoint 2 updates? Instructions are given in the slack channel.

[rupeshknn]

Checkpoint 2

Implemented Lanczos Ground state algorithm for scipy CSR sparse matrices and fixed bugs to work with complex arrays. Runtime comparable with QuSpin and better than SciPy.sparse and NumPy.

We are now working on time evolution using Lanczos and sparse expm.

[rupeshknn]

Forgot to add the final presentation. Sorry. Final-Lanczos_Algorithm_for_Qiskit_Dynamics.pdf

[rupeshknn]

A late update, but the PR has been merged. 🎉

https://github.com/Qiskit/qiskit-dynamics/pull/109