luca ion

Solving multi-particle systems is an important topic in quantum chemistry and condensed matter physics. In this article I focus on finding the ground states and ground state energies for the He-H+ and H2O molecules using the power of quantum computing. I will be using a variational quantum eigensolver algorithm (VQE) which will run on both a simulation of a quantum computer and on the IBM quantum computer. I will compare the results against the exact ground state energy found through other classical means. The H2O simulations were run on Nottingham's High Performance Computer (HPC).

Our Universe can modelled by various scalar fields inside potential wells V. These potentials can have two local minima, one lower in potential (true vacuum) than the other (false vacuum). Given that some field is in the false vacuum, it will want to go to the true vacuum; classically this can only happen if additional energy is provided in order for the field to overcome the potential barrier, however quantum mechanically we know that tunnelling is also possible. This tunnelling can be thought of as the creation of a bubble where inside the bubble the universe is in the true vacuum, and outside its in the false vacuum. We calculated the probability of such tunnelling event and the radius of the bubble, analytically, under certain limits. We then calculated the same quantities numerically and were able to successfully match the numerical and analytic computations via plots done in python.

Many-body physics benefits from the power of quantum computing. We are interested in building quantum circuits that can approximate the ground states of several Hamiltonian models, some of which cannot be solved exactly. We devise an optimization algorithm that will compute the necessary gates that make up the quantum circuit that will approximate the ground state. Once we have the approximated states, we compute different correlation functions on both the exact ground state and the quantum circuit approximation in order to learn more about the quantum circuits. All the computations in this paper are carried out using Python and NumPy. In addition, the use of Nottingham's HPC was used for the more computationally demanding tasks. We find that measuring a variety of correlation functions on our approximated state gives us a good approximation of the state we are trying to approximate. Moreover, with the help of these measures, we get more insights into the quantum circuit structure.