ADAPT-VQE and its application to Nuclear Physics

Abstract

The simulation of quantum mechanical systems is one of the main applications of quantum computers. Variational Quantum Algorithms, VQA tries to adapt to the limitations of NISQ devices, in contrast to the initially developed algorithms for this purpose (Quantum Phase Estimation, QPE), which were designed to be deployed in a fault-tolerant quantum computer. Variational Quantum Eigensolver, or VQE, is the first in the class of VQAs to achieve quantum advantage. The choice of ansatz can determine whether a VQE is successful (or unsuccessful); for example, a very deep ansatz can compromise short-term viability and make the algorithm ineffective. This dissertation sought to investigate various ansatz by analyzing their noise-resilience and feasibility in cutting-edge quantum computers. Dynamic ansatz, ADAPT-VQE was specifically investigated, and their performance was contrasted with that of predefined ansatz, Hardware efficient ansatz. Hardware-efficient-VQE (static) and ADAPT-VQE (dynamic), were implemented in simula tors and fake backends. The impact of shot count and optimizer on the ansatz was studied. The effect of noise on convergence, along with its mitigation, was evaluated. The significance of the different operator pools in ADAPT-VQE was also examined.