The scale of the problem
Today's encryption algorithms can be broken. Their security derives from the wildly impractical lengths of time it can take to do so.
Let's say you're using a 128-bit AES cipher. The number of possible keys with 128 bits is 2 raised to the power of 128, or 3.4x10^38, or 340 undecillion. Assuming no information on the nature of the key (such as that the owner likes to use his or her children's birthdays) a code-breaking attempt would require the testing of each possible key until one is found that works.
Assuming that enough computing power was amassed to test 1 trillion keys per second, testing all possible keys would take 10.79 quintillion years. This is about 785 million times the age of the visible universe (13.75 billion years.) On the other hand, you might get lucky in the first 10 minutes.
Using quantum technology with the same throughput, exhausting the possibilities of a 128-bit AES key would take about six months. However, moving to 256 bits would give the system a level of security equivalent to 128 bits with a conventional computer.
Cracking an RSA or EC cipher with a quantum machine would be essentially immediate.