# Qiskit Runtime VQE

(07/02/2021)

## Variational Quantum Eigensolver

VQE is one of the key algorithms that focus on making the best of existing quantum computers (NISQ). It solves a difficult quantum problem with broad applications that will transform chemistry and material design. The problem, (finding the lowest energy level of a quantum system), is crucial for understanding the structure of molecules and the behavior of novel materials. It is very difficult for classical computers to tackle this problem without methods that use a lot of approximations, and extensive computing power. The ground state of a quantum system is also known as the lowest energy eigenvalue.

VQE was designed to solve this problem without requiring long circuit depths. This is a fast way to answer difficult chemical physics questions with current quantum computers. A more in depth tutorial can be found here.

VQE is iterative, relying on tightly-bound classical computing and quantum computing parts that vary parameters trying to approximate the correct solution.

Roughly, these are the steps of a VQE iteration.

- First, make a guess, also known as an ansatz, for the trial solution to the ground state of the quantum system. This guess can be anything, but the better it is, the better the performance. New methods focus on improving how to make more clever guesses on classical computers.
- The guess is parameterized and then used to construct the inputs for the quantum algorithms. The quantum computer then calculates components of the energy corresponding to this trial.
- These energy components are then sent to the classical computer. It uses clever techniques to use the parameters to "wiggle" the state and come up with a new guess for the trial ground state. There is a lot of fruitful research also on clever wiggle methods.

As this process goes on, each iteration should start to approach the correct solution. In our VQE example, this looks like this:

VQE has applications beyond chemistry, and is a great place to start to squeeze more power out of today's quantum computers.

You can read more about how to use Qiskit Runtime at Strangeworks here.