# GPU implementation of the Hierarchical Equations of Motion

The Hierarchical Equations of Motion (HEOM) method is a non-perturbative approach to simulate the evolution of the density matrix of dissipative quantum systems. The underlying equations are a system of coupled ODEs which can be run on a GPU. This will allow the study of larger systems as discussed in [1]. The goal of this project would be to extend QuTiP’s HEOM method [2] and implement it on a GPU.

Since the method is related to simulating large, coupled ODEs, it can also be quite general and extended to other solvers.

## Expected outcomes

- A version of HEOM which runs on a GPU.

- Performance comparison with the CPU version.

- Implement dynamic scaling.

## Skills

- Git, python and familiarity with the Python scientific computing stack

- CUDA and OpenCL knowledge

## Difficulty

- Hard

## Mentors

- Neill Lambert (nwlambert@gmail.com)

- Alex Pitchford (alex.pitchford@gmail.com)

- Shahnawaz Ahmed (shahnawaz.ahmed95@gmail.com)

- Simon Cross (hodgestar@gmail.com)

## References

[1]

https://pubs.acs.org/doi/abs/10.1021/ct200126d?src=recsys&journalCode=jctcce

[2]

https://arxiv.org/abs/2010.10806