Quantum Variational Optimization and Adiabatic Methods

Abstract

In this chapter, we will take a look at the various optimization techniques that use quantum computing in their formulation. A couple of such algorithms that we are going to work through in great detail are the variational quantum eigensolver, popularly known as VQE, and the quantum approximate optimization algorithm, also known as QAOA. The central idea in both methods is to define cost objectives as an expectation of appropriate Hamiltonians pertaining to quantum systems. Based on the maximization or minimization problem, we look to derive the maximum or minimum eigenvalue state through these optimization techniques. Both of these methods are variational in that they combine both quantum and classical methods for the optimization. Since the topic is centered around Hamiltonians, we will study the popular Isling Hamiltonian model as well in this chapter. Similarly, the QAOA technique is based on the adiabatic evolution of a quantum system, and hence we will study its underlying math in great detail in this chapter.