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Benjamin Neumann
2026-07-29 09:23:16 +02:00
parent 993f092b4a
commit 46cbcaa733
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.obsidian/workspace.json
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SS2026/Quantum Computing/3. Quantum Systems/Quantum Systems.md
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## Classical possibilities
finite
all outcomes for a quantum system
`Random bit generator with 1 bit output = classical possibilities 0 and 1`
## Quantum States
State of quantum system as vector
-> each entry = classical possibility
-> called amplitude
-> can be negative and are complex numbers
Amplitudes tell us the probability of quantum state being in the corresponding class. poss.
probability = |amplitude|^2
$Pr[x] = |\psi|^2$
Also: $\sqrt{\sum^n_{i=1} |\psi|^2} = 1$
Example:
![[Pasted image 20260729091741.png]]
## Unitary transformation
![[Pasted image 20260729092010.png]]
Example with Pauli-matrices:
![[Pasted image 20260729092121.png]]