Variational Quantum Eigensolvers with Qiskit

This project aims to demonstrate applications of the VQE algorithm towards Chemical modeling. The contained tutorials were created to supplement a final project for PHYS 660: Quantum Information and Computation. Here are slides from our final presentation.

Motivation Examples

Within tutorials/VQE.ipynb, we have written up motivating examples to find the ground state energy of a single and two qubit system Hermitian operator.

The single qubit VQE optimizations use the U3 gate based variational form, as shown below [1].

While the two qubit VQE optimizations use a variational form derived from Shende et al. [1-2].

Ground State Energy of Small Molecules

Also within tutorials/VQE.ipynb, we have used Qiskit Aqua and Qiskit Chemistry to solve for the ground state energy of Li-H and H-H at various interatomic distances. These VQE optimizations were seeded with Hartree-Fock ansatz.

Here are the main results.

Next Steps

We hope to later simulate VQE optimizations on noisy systems with error mitigation. Please check out our slides to learn more!

References

1. Simulating Molecules using VQE Qiskit Tutorial
2. Shende, Vivek V., Igor L. Markov, and Stephen S. Bullock. "Minimal universal two-qubit cnot-based circuits." arXiv preprint quant-ph/0308033 (2003).