7.2 Introducing VQE
The goal of the Variational Quantum Eigensolver (VQE) is to find a ground state of a given Hamiltonian . This Hamiltonian can describe, for instance, the energy of a certain physical or chemical process, and we will use some such examples in the following two sections, which will cover how to execute VQE with Qiskit and PennyLane. For the moment, however, we will keep everything abstract and focus on finding a state such that is minimum. Note that in this section, we will be using to refer to the Hamiltonian so that it does not get confused with the Hadamard matrix that we will also be using in our computations.
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VQE is by no means the only quantum algorithm that has been proposed to find the ground states of Hamiltonians. Some very promising options use a quantum subroutine known as Quantum Phase Estimation (QPE) (see, for instance, the excellent surveys by McArdle et al. [66] and by Cao et al. [22]). The main disadvantage of these approaches...
