In the quantum computation

lectures of this MOOC we have introduced a few areas

where quantum computation may be used. In these examples, quantum computers can become

exponentially faster than their classical counterparts. Next to the discussed areas,

there are quite a few other examples where quantum computers may become very useful,

and I will mention some of them. One such example is related to searching databases. Here Grover’s algorithm could be very valuable. Grover’s algorithm is a quantum algorithm

to perform a search on an unstructured database. You may want to find your name

in a large unsorted database. If you have a classical computer,

it can actually be pretty difficult to find out. Instead, if you would have a quantum computer

that can run Grover’s algorithm, then you could find it in a quadratic time shorter. This is not an exponential difference, but it can save

a very significant time once the database is large. Now suppose you are in a maze,

and you want to find the exact exit. If you would be using a classical computer,

this could take a long time, because a computer will explore each path at a time. However, if you could make use of a quantum

computer and run Grover’s algorithm, you could exploit the phenomena

of entanglement and superposition. In this way, you will find your way out much faster. There are many more possible applications

in the area of for example optimization. To mention a few areas: quantum approximate

optimization, semidefinite programming, matrix powers, quantum annealing. All these applications have their own caveats

and they all are challenging. But if we can solve them,

the impact can be enormous. We are now in a very exciting time, where progress

is made quickly and almost on a daily basis. So we envision that soon

some of these applications will find reality. We could imagine that by using quantum computers

themselves, we will even find new applications and new focus areas, and we will probably

only find out the full power of quantum computation once we have built actually built a quantum computer.