Quantum computers are mostly theoretical. Some simple versions have been built but the technology is unstable.
You should remember in the double slit experiment that electrons fired at a wall with two slits in it give the appearance of going between both slits and interfering with itself. Quantum computer rely on the ability of sub-atomic particles, like electrons, to simultaneously exist in multiple states. The idea is that they'd be able to use each of the multiple states as a separate processor. No, that's not quite right. They'd be able to calculate multiple solutions at the same time. The answer returned would not be a hard yes/no answer like with current binary computers. Answers would be more like pie charts listing all the possibilities and how often certain answers popped up. This isn't an accurate description, but I'm not sure how to put the more technical answer in layman's terms.
Current computer encryption codes can get up to 128 bits. If you don't have the decryption code your grandchildren would have to get the answer for you. A quantum computer should be able to get the answer back to you in a few hours.
WHY am I telling you all of this? Why have I spent three lessons giving you the broad strokes of quantum physics? Because more and more these fundamentals are key in various science fiction stories.
In the Hominids/Humans/Hybrids trilogy Neanderthals are experimenting with a quantum computer. They're calculating larger and larger numbers causing the individual quantum processors to reach into more and more parallel realities where other quantum computers exist. When the numbers got too big the computer reached into a reality where there wasn't a quantum computer. They reached into our reality.
In "Calculating God" there's an alien race that spends almost all it's time in prayer. Remember how putting an observation device at one slit made the electron pass through only one slit? By the aliens' thinking God is the observer so God determines which of the many universes is real. Only by constant prayer can they keep God watching their universe and continue making their reality THE reality.
In the Discworld series there have been a few references to the Heisenberg Uncertainty Principle (which I haven't explained yet) influencing leopards that move so fast they can't know who they are and where they are at the same time.
Even Star Trek seriesesesees have mentioned the need for Heisenberg Compensators to fix the nebulous nature of individual electrons when scanning the person to be transported.
For you and me it's just a curiosity that makes life a bit more interesting.
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