Chapter 7
VQE: Variational Quantum Eigensolver

From so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
— Charles Darwin

In the previous chapters of this part of the book, we have studied how quantum algorithms can help us solve combinatorial optimization problems, but there are many other important types of optimization problems out there! This chapter will broaden the scope of our optimization methods to cover more general settings, including applications in fields such as chemistry and physics.

We will achieve this by studying the famous Variational Quantum Eigensolver (VQE) algorithm, which can be seen as a generalization of the Quantum Approximate Optimization Algorithm that we studied back in Chapter 5, QAOA: Quantum Approximate Optimization Algorithm. Actually, it would be more precise to say that we can see QAOA as a particular case of VQE; in fact, VQE was introduced earlier than QAOA in a now famous paper by Peruzzo...