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]]