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ObsidianVault/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