Classic computers work on the possible solutions for a problem one by one and one after the other, but quantum computers are capable of working on all the possible solutions for a problem at a single time, so quantum computers are faster at solving complex problems than classic computers.
Take, for example, cryptography. The goal is to find the factors of large integers. In classical computers, the most efficient way to solve this problem is to divide the integer by every number smaller than its square root to see which numbers will factor it.
In this approach, as more digits are added to the integer, the time required for this test grows very rapidly. But with a quantum computer, factorization is a snap because the test on all numbers less than the square root of the integer can be performed simultaneously, so only a single test is needed to find the right answer.
