Quantum computing is a lot to wrap your mind around. To put things very simply (as Canadian Prime Minister Justin Trudeau did recently, with surprising eloquence) regular computers are made up of bits—ones and zeros—which are fed into logic gates and come out the other side either transformed or the same, as another one or zero. Computers get faster as you make these gates smaller and fit more into one place. But in quantum computing, this entire process goes out the window.
For a slightly more in-depth explanation, you can try this new video from the excellent PBS Infinite Series YouTube channel, that digs into the crazy math behind quantum computers. As the host, Kelsey Houston-Edwards, is quick to point out, quantum computers don't actually exist yet, but math backs up the possibility of building them in the future.
Quantum mechanics allows for particles to exist between two states, in what's called a superposition. These particles only settle into one state or the other when measured—think of Schrödinger's cat. Quantum computers apply this to bits, which in this case are called qubits. In one of these theoretical computers, a qubit fed through a logic gate (in quantum computing, a quantum gate) exists in a superposition, meaning it is neither one nor zero before it's measured.
When we collapse the superposition of a qubit enough times, we find an equation that describes its superposition, the probability that it will result in a zero or one. Why does this matter? Because when we run a function on a string of zeros and ones in a classic computer, we can only change the states of each bit in one way at a time. In quantum computers, because the qubits are held in superpositions where they are in infinitely many states at once, the computer is able to hold an insane amount of information without us ever needing to see it until we want a final answer. We can work with the probabilities given to us by superpositions without dealing with the dozens of digits-long numbers that those equations represent.
For example, the number of states possible in a string of six bits is two (the number of possible states for each bit) to the sixth power, or 64 in total. This means that to figure out all the possible states of the bits with a regular computer, it would take up to 64 steps. But when we use superpositions of qubits to find the probability of different answers to this function, we don't figure out the actual state of each qubit, just the probability of them existing in each state, and getting to the final equation only requires four steps. If you imagine this applied to much, much longer strings of zeros and ones, you can begin to see how much quantum computing may be able to speed processing speeds.
There's plenty more to it than just that of course, and Houston-Edwards gets into the mathematics that allow all of this to function, which requires imagining hyper-dimensional spheres and all kinds of other wacky stuff. It's a lot of fun to think about the possibilities here—we'd just recommend drinking a cup of coffee, or three, first.
Source: PBS Infinite Series