# 10

Variational Quantum Eigensolver

Parameterised quantum circuits can find many possible applications outside the quantum machine learning use cases considered in the previous chapters. They can be used to solve problems as diverse as portfolio optimisation [168] and protein folding [248]. However, one aspect remains the same regardless of the specifics of the particular algorithm: the construction of a quantum state with desired characteristics through an optimal PQC configuration (ansatz) and an optimal set of adjustable PQC parameters. This, in turn, is done through the minimisation of some cost function – it can be a classification error in the case of a QNN-based classifier or a distance between two distributions in the case of QCBM.

The Variational Quantum Eigensolver (VQE) is a PQC-based algorithm that aims to find the smallest eigenvalue (the lowest energy) of a problem Hamiltonian. As we know from Chapter 3, the objective functions of many...