The description of interacting particles, subject to quantum effects, is known as the many-body problem. Its exact resolution faces the exponential growth of the required computational resources with the number of degrees of freedom considered. Among the developments aimed at tackling this problem and pushing beyond current limits, quantum computing represents a promising approach. Notably, the variational quantum algorithms, hybrid quantum-classical algorithms that are more resilient to errors than their purely quantum counterparts, are particularly interesting to tackle the many-body problem with currently available quantum platforms.
This thesis investigates the application of such algorithms to the nuclear many-body problem. Several generalisations of the ADAPT-VQE hybrid algorithm are presented to approximate the ground state of a quantum many-body system. Their performances are benchmarked and compared in a simulation, with an application to the pairing model, which allows to study superfluid systems such as atomic nuclei. The resulting ground state approximations constitute the starting point of another hybrid computing procedure designed to evaluate Green’s functions of such systems. This procedure has been simulated and validated within this test model, and the required quantum resources have been quantitatively estimated.
These results have been obtained with emulators of ideal digital quantum computers. However, current quantum computers remain limited by noise, and to consider their short-term use, it is necessary to take into account their technical constraints. To this purpose, analog quantum computing is more adapted than digital quantum computing. Hence, in the second part of this thesis, the focus has been on neutral atom quantum computers, which are naturally adapted to analog quantum computing. Their use with variational procedures raises different obstacles and limitations. Several methods are presented here to lift these difficulties, resulting in a protocol intended for the computation, on these machines, of the ground state of a simple model of the deuteron. A complete methodology has been developed with the goal of testing it on current and future neutral atom quantum computers.
LENA laboratory – Structure of the Atomic Nuclei – Laboratoire d’Etudes du Noyau Atomique (LENA)
Groupe Théorie Nuclear Structure Theory
DPhN, LENA