# Solving linear equations with quantum computers

Already in high school, we learn about simple linear equations with two axes, two variables, a nice line passing through some points. But did you know that many of the scientific and engineering problems which affect our daily lives can be addressed by solving linear equations?

Solving these linear equations can be very complicated when the number of variables is large, as it is for industrial-scale problems. In this video, we will introduce linear systems, as well as a quantum algorithm that has the potential to solve them much faster than their classical counterparts.

## Prerequisite knowledge

- Basic linear algebra

## Further thinking

In the video, Menno Veldhorst discussed that the solution vector of the system is not an output of the HHL algorithm. In other words, we need to “ask a quantum mechanical question” to this output vector to obtain some information about the solution of our problem. This way, quantum algorithms are significantly different from classical algorithms, where we immediately get the answer to our problem.

In fact, this is true for many quantum algorithms in general. So what do you think is the main challenge in constructing quantum algorithms?

## Further reading

Menno introduces the HHL algorithm in the video. Are you interested in reading the actual paper where this algorithm is presented? Take a look!

Otherwise, the Wikipedia page of the subject gives an excellent introduction to how the algorithm really works. Make sure you know about bra-ket notation before clicking!

If you rather want to watch another video about the algorithm, Peter Wittek from the University of Toronto gives a 5 minute explaination here: