◄Previous: 1.1 What can classical computers do?

1.2 What can quantum computers do?

Quantum computing offers a new computing approach that is based on the idea that the rules of quantum mechanics can allow shortcuts to solutions for certain tasks. There are quantum algorithms with polynomial run-times that can solve problems where the only known classical algorithms have exponential run-times. Quantum computers make use of the fact that quantum states can be made of linear combinations of individual states and when a measurement is taken, one of the individual states will be measured with a given probability. You will see that entanglement is another fundamental resource for quantum computing.

The integer factorisation problem, which seeks to find the prime number factors of an n-digit integer, is of particular interest because it is the basis of a lot of information security. The run-time of the classical algorithm scales exponentially so as n increases a classical computer takes longer and longer to factorise the integers as n increases. The integer factorisation problem is an example of a a problem that quantum computers can solve much more efficiently. If quantum computing was able to solve the integer factorisation problem with a polynomial run-time then there would be a major problem for information security.

Another example of a problem with an exponential run-time is the travelling salesperson problem, which seeks to find the shortest route between a number of cities subject to visiting each city only once and returning to the starting city at the end of the journey (see Figure 2). This is a typical optimisation problem which can be used to demonstrate the power of quantum computing as well as being a problem which delivery companies would like to be able to solve quickly.

Figure 2 An illustration of the travelling salesperson problem. The image on the left shows 7 cities (in blue) and a trial of all 360 possible routes between them (in red). The image on the right shows the optimum distance after trialling all possible routes.

Exercise 2

Write a sentence or two to summarise in general terms the context in which quantum computers are considered to be an improvement on classical computers.

(A text entry box would appear here, but your browser does not support it.)

Answer

Your answer will not be the same but a possible answer is:

Quantum computers may be able solve some problems more quickly than classical computers if problem solving algorithms which have exponential run-times on a classical computer can be written to have polynomial run-times on a quantum computer.

Your answer should include the same conclusions.

◄Contents►Next: 2 Background mathematics and terminology

OpenLearn - Introduction to quantum computing
ou logoCreative Commons non-commercial share alike icon Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.