Benjamin/ObsidianVault
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

vault backup: 2026-07-28 16:27:30

Browse Source
This commit is contained in:
Benjamin Neumann
2026-07-28 16:27:30 +02:00
parent 6aeddcf500
commit 0f230a29dd
1 changed files with 6 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files
SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md
+6 -2
View File
@@ -4,6 +4,10 @@ All the different possible outcomes.
### Probability distribution ### Probability distribution
A Probability for each possibility: Pr[x] = p where p $\in$ [0,1] A Probability for each possibility: Pr[x] = p where p $\in$ [0,1]
`For a coinflip this would be Pr[Heads] = 1/2 and Pr[Tails] = 1/2` `For a coin flip this would be Pr[Heads] = 1/2 and Pr[Tails] = 1/2`
Combine all probabilities for all possible outcomes as vector to get probability distribution+ Combine all probabilities for all possible outcomes as vector to get probability distribution+
A valid distribution d has $\sum d_i = 1$ and for all i is $d_i \geq 0$ A valid distribution d has $\sum d_i = 1$ and for all i is $d_i \geq 0$
For a coin flip the probability distribution would be $d_coin \in \mathbb{R}^2$ with $d = (1/2, 1/2)^t$
### Probabilistic processes
A probabilistic process is a Matrix A $\in$ $\mathbb{R}^{N \times N}$ if every column of A is a valid probability distribution