This repository contains the Jupyter notebooks with the results discussed on the author’s paper Hamiltonian Minimization in the NISQ Era. This paper outlines the use of noisy intermediate-scale quantum (NISQ) computers for Hamiltonian minimization problems. We delve into the mathematical formulation of Variational Quantum Eigensolver (VQE), Quantum Annealing (QA) and Quantum Approximation Optimization Algorithm (QAOA), with computational results for a 3-qubit minimization problem and its extension to 6-qubit, 13-qubit and 140-qubit. We show how different initial parameters leads to optimal, less accurate, or no satisfactory solutions using the considered versions of VQE and QAOA, a well known challenge. For all problems, the optimal solution was found using QA and hybrid solvers. This work serves as a hands-on approach to understand quantum annealing, variational quantum algorithms, quantum hardware limitations and current landscape.

The reader needs to create an account on the following clouds:

Dwave Leap

IBM Quantum

Quafu

and save the api token on the corresponding notebook in order to run them. For Dwave's API token set up see Set Up Your Environment.

Install requirements locally (ideally, in a virtual environment):

pip install -r requirements.txt

R. Pereira da Silva (2023), Hamiltonian Minimization in the NISQ Era, SSRN Electronic Journal

Released under the Apache License 2.0. See LICENSE file.