vault backup: 2026-08-06 20:31:26

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

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+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]]