# Cloning for error correction by preparing state multiple times

In quantum error correction, we start with the fact that no-cloning theorem doesn't allow cloning of unknown states, hence we need to come up with other strategies.

But often we know the circuit that produces the state that we want to protect, so can't we just prepare the same state multiple times to in-effect clone it?

I realize that the circuits used for preparation would themselves incur error. But wouldn't there be a way to go around it by using more copies?

Is there a precise way to see that this pursuit is completely useless - perhaps one could show that there is no way to do this without using an exponential number of copies?

• Does this answer your question? Copying |0⟩, |1⟩ Qubits will break the no-cloning theorem? Aug 31, 2022 at 14:05
• No, not really. I know that we could copy a known state. My question is - why can't we use this fact to create the redundancy needed for quantum error correction. Aug 31, 2022 at 16:12

• @user1752323 Honestly I just wildly assumed it'd be $\ln(n)$ times bigger because of pattern matching to other problems like coupon collector. I did a quick simulation using numpy and it seems to be right. It's maybe much clearer using an argument based on half lives, where it's 40 times longer because after 40 half lives you've got 1 in $2^{40} \approx$ 1 in a trillion of the copies left. Sep 1, 2022 at 19:49