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Quantum Error Correction/Quantum Error Correction.md +++ b/SS2026/Quantum Computing/17. Quantum Error Correction/Quantum Error Correction.md @@ -0,0 +1,30 @@ +One of the biggest challenges in quantum computing is noise. +As an Example, when we apply a unitary, this unitary might not behave exactly as expected. + +Classically, error correction uses some kind of error correcting code which, in turn, must also be transmitted over a noisy channel. + +![[Pasted image 20260806110847.png]] + + +## Repetition codes + +The simplest classical error correcting code is repetition. +If we send the bit 0, we repeat it 3 times, same for 1. 0 = 000, 1 = 111. +Hamming abstand 3 = 1 bitfehler korrigieren. + +In a quantum system we can't just look at (measure) our system to repeat it. + +### Bit Flip Code + +![[Pasted image 20260806111316.png]] + +Note that we cant just measure if an error has occurred, so we use this circuit: + +![[Pasted image 20260806111448.png]] + +### Phase Flip Code + +Correcting Z-errors is possible with this: + +![[Pasted image 20260806111549.png]] +