This is my submission for the QOSF 2020 mentorship program. I have demonstrated the variational quantum eigensolver (VQE) algorithm, by using it to find the lowest eigenvalue of a toy Hamiltonian.

A detailed demonstration is given in VQE_analysis.org. Github does not properly render Org files. You can either use an editor that supports Org, like Emacs, or you can view the HTML export on my blog. The second option might be the easiest. The same results can also be generated by executing python3 main.py. I have only tried this on a GNU/Linux device, cannot guarantee if it will run without modifications on a Windows/MacOS device.

The implementation of the algorithm is spread across three files in the vqe folder:

1. vqe.py: This file provides a base class to define ansatzes, and two two-qubit ansatzes that I have used in the demonstration. It also provides functions to compute expectation values of Hermitian operators, using a quantum computer, or a quantum simulator.
2. utils.py: This file provides a function to decompose Hermitian operators into tensor products of Pauli matrices.
3. optimizers.py: This file provides an implementation of the SPSA optimization algorithm. I plan to add additional optimization algorithms which can be used to solve small toy problems like this.

I have used Qiskit to implement the quantum part of the algorithm. To run this on your device please install the necessary dependencies. You can easily do it with pip install -r requirements.txt, preferably in a Python virtual environment.