Chapter 5: Variational Quantum Eigensolver (VQE) Algorithm
![](https://static.packt-cdn.com/products/9781803243900/graphics/image/B18268_Figure_5.1.jpg)
Figure 5.1 – Steepest descent line on a potential energy surface (PES) [authors]
We introduced the history behind the use of the variational method in Section 1.1, Understanding the history of quantum chemistry and mechanics. It is a mathematical construct that can be used computationally. Within the context of quantum chemistry, the variational method is used to determine the lowest energy associated with an eigenvalue, either the ground state or excited states.
The Variational Quantum Eigensolver (VQE) algorithm was introduced in 2014 [VQE_1] and is defined using quantum-based hardware. It is the first of several Variational Quantum Algorithms (VQAs) that are currently being explored by the scientific industry.
We use Unitary Coupled Cluster Singles and...