vault backup: 2026-08-07 11:09:14

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SS2026/Mathematische Logik/Einleitung/Einleitung.md

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+Logik ist die Lehre des vernünftigen Schließens.
+
+Zentrale Fragen:
+- Wie lassen sich Sachverhalte beschreiben? SYNTAX
+- Was bedeuten diese formalen Aussagen? SEMANTIK
+- Wie lassen sich Schlussfolgerungen ziehen und beweisen? INFERENZ
+
+

SS2026/Mathematische Logik/Mathematische Logik.md

@@ -0,0 +1,10 @@
+## [[Einleitung]]
+## Rekursion und Induktion
+## Aussagenlogik
+## Folgern und Beweisen
+## Strukturen
+## Logik der 1. Stufe
+## Der Vollständigkeitssatz
+## Unentscheidbarkeit der Logik der 1. Stufe
+## Elementare Äquivalenz
+## Ausblick

SS2026/Mathematische Logik/Notation/Notation.md

@@ -0,0 +1 @@
+![[log-appA.pdf]]

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

@@ -0,0 +1,43 @@
+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]]
+
+
+## Shor's code
+
+The error correcting code for XZ-errors is called Shor-code.
+
+![[Pasted image 20260806113147.png]]
+
+![[Pasted image 20260806113154.png]]
+
+
+## Steane Code
+
+![[Pasted image 20260806113212.png]]

SS2026/Quantum Computing/18. Fault-torerant computation/Fault-Tolerant Computation.md

@@ -0,0 +1,29 @@
+
+We now face two problems with continuous computations:
+1. Applying operations on logical qubits. Applying operations on encoded qubits would only be possible by decoding - applying - encoding again. Not optimal. Also errors can happen in decode encode.
+2. Operations on encoded qubits could introduce new more complex errors.
+
+
+## Operations on logical/physical qubits
+
+We begin by defining how to apply operations to encoded qubits:
+
+![[Pasted image 20260806135601.png]]
+![[Pasted image 20260806135610.png]]
+
+
+## Fault tolerant Gates
+
+Now we need to reduce our error probability.
+
+![[Pasted image 20260806140451.png]]
+
+To make this circuit fault-tolerant, we replace it with:
+
+![[Pasted image 20260806140514.png]]
+
+Let's look at a circuit for CNOT:
+
+![[Pasted image 20260806140629.png]]
+![[Pasted image 20260806140639.png]]
+![[Pasted image 20260806140650.png]]

SS2026/Quantum Computing/19. Quantum Complexity/Quantum Complexity.md

@@ -0,0 +1,29 @@
+We start with the common class NP (Non-deterministic polynomial time)
+
+![[Pasted image 20260806202511.png]]
+*Some details omitted
+
+![[Pasted image 20260806202558.png]]
+
+Question: can quantum computers solve SAT in polynomial time? (and by that, all problems in NP?)
+
+
+## Oracle lower bound
+
+![[Pasted image 20260806202735.png]]
+
+![[Pasted image 20260806202805.png]]
+![[Pasted image 20260806202815.png]]
+![[Pasted image 20260806202822.png]]![[Pasted image 20260806202829.png]]
+
+## Quantum Merlin Arthur
+
+Is there a "quantum NP"?
+
+We define the class QMA (Quantum Merlin Arthur):
+
+![[Pasted image 20260806203005.png]]
+
+Example of a QMA Problem: Local Hamiltonian Problem
+
+![[Pasted image 20260806203055.png]]

SS2026/Quantum Computing/Introduction to Quantum Computing.md

@@ -15,3 +15,5 @@
 ## 15. [[Ion-based Quantum Computers]]
 ## 16. [[Universal Set of Gates]]
 ## 17. [[Quantum Error Correction]]
+## 18. [[Fault-Tolerant Computation]]
+## 19. [[Quantum Complexity]]