The best I understand it, quantum computing relies on the weird ability of electrons to be "neither here nor there" to create a tri-state bit: 0, 1, or 2. By working in ternary instead of binary, data can be processed at much higher speeds (and stored in less memory space).
The hardware difficulty with quantum computing is that you have to keep things at darn near 0 Kelvin, so the electron's "neither here nor there" state can actually stay locked in place.
At least, that's the "explain like I'm 5" explanation.
Although this "ternary" explanation is simple and seems to provide some intuition about why a quantum computer is faster, it's incorrect. Quantum bits are fundamentally different from binary and ternary bits.
Ternary bits are actually possible in classical computers. Ternary bits are (almost) never used because reliable binary bit hardware was developed first.
Some people have built ternary computers which are super cool though!.
Here's a simple explanation of quantum bits that is totally true, but unfortunately doesn't provide much intuition, or help you understand why quantum is faster than classical: A quantum bit is a pair of real numbers (let's call them a and b) such that a2 + b2 = 1. That's it. The simple and somewhat unsatisfying fact is that normal intuition doesn't really apply to quantum computing.
Here's a fantastic video that explains how a quantum bit leads to quantum speedup, entanglement, and quantum teleportation using the math.
I know less about quantum computer hardware, but your hardware difficulty explanation seems on point.
I certainly had picked up some incorrect information, then. Thanks for the insight!
No worries, and thanks for your original comment. I think it's great to talk about common misunderstandings, that way everyone comes out with a better understanding.
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