> by default repetition makes things worse instead of better
Can you elaborate on this a bit? My intuition is that, by default, statistical models benefit from larger N. But I have no experience in quantum physics.
It's because unintended measurement is a type of error in a quantum computer. Like, if an electron passing near your qubit would get pushed left if your qubit was 0 and right if was 1, then you will see errors when electrons pass by. Repeating the 0 or 1 a thousand times just means there's 1000x more places that electrons passing by would cause a problem. That kind of redundancy makes that kind of error mechanism worse instead of better.
There are ways of repeating quantum information that protect against accidental measurement errors. For example, if your logical 0 is |000> + |110> + |011> + |101> and your logical 1 is |111> + |001> + |100> + |010> then can recover from one accidental measurement. And there are more complex states that protect against both bitflip errors and accidental measurements simultaneously. They're just more complicated to describe (and implement!) than "use 0000000 instead of 0 and 1111111 instead of 1".
Classical systems: You measure some state, with the measurement containing some error. Averaging the measurement error usually gets closer to the actual value.
Quantum systems: Your measurement influences/can influence the state, which can cause an error in the state itself. Multiple measurements means more possible influence.
Yeah that's roughly it. In classical computers all errors can be simplified as being bit flip errors (0 instead of 1, 1 instead of 0). Like, power loss is a lot of bit flip errors that happened to target the bits that should have been 1. In quantum computers this simplification does not work, there is another type of error called a phase flip. Measurements cause phase flip errors. You can exchange the phase flip and bit flip bases by using a gate called the Hadamard gate. So if you surround measurements with Hadamard gates, you will see bit flip errors. The existence of gates like Hadamard is what makes it possible to see these kinds of things at all, and correspondingly its availability can be thought of as the thing that makes a quantum computer a quantum computer, instead of a classical computer.
If there's interference, could you do something like when using 7 repetition for each bit, take whatever 5 of 7 is, e.g. 1111100 is 1 and 1100000 is 0.
It actually depends how this sentence is intended. There exist quantum repetition codes: the Shor code is the simplest example that uses 9 physical qubits per logical qubit. Since the information is quantum it needs majority voting over two independent bases (hence 3x3=9 qubits to encode a logical one).
You might be making the mistake of thinking that quantum mechanics runs on probabilities, which work in the way you are used to, when in fact it runs on amplitudes, which work quite differently.
Can you elaborate on this a bit? My intuition is that, by default, statistical models benefit from larger N. But I have no experience in quantum physics.