vault backup: 2026-08-06 11:15:53

.obsidian/workspace.json

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SS2026/Quantum Computing/17. Quantum Error Correction/Quantum Error Correction.md

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+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]]
+