Quantum computing has long confused and challenged the best of us. You can read only so many technical details before your head explodes. Yet it’s likely that usable quantum cryptography will be a fact of life within the decade — and that has huge ramifications.
Most of today’s popular cipher algorithms (especially public/private key exchanges) work because the math involved is very difficult for conventional (nonquantum) computers to solve. Take some really big prime numbers, add, subtract, multiply, and divide them a bit (like you do with the RSA algorithm), and you quickly get a mathematical problem that is very hard to solve even with hundreds of billions of guesses.
But conventional cryptography would be rendered useless if someone either came up with a very, very speedy computer or learned a method to do the math exponentially faster than the methods we have today for solving crypto problems.
Quantum computers are that solution — or problem, depending on how you see it.