vault backup: 2026-07-30 14:49:26

.obsidian/workspace.json

@@ -216,6 +216,8 @@
   },
   "active": "25f5b25d5eca7203",
   "lastOpenFiles": [
+    "SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge/Pasted image 20260730144713.png",
+    "SS2026/Quantum Computing/Bernstein-Vazirani/Anhänge",
     "SS2026/Quantum Computing/Introduction to Quantum Computing.md",
     "SS2026/Quantum Computing/Anhänge/Introduction-to-Quantum-Computing.pdf",
     "SS2026/Quantum Computing/Bernstein-Vazirani/Bernstein-Vazirani Algorithm.md",
@@ -242,7 +244,6 @@
     "SS2026/Quantum Computing/6. Composite Systems/Anhänge",
     "SS2026/Quantum Computing/6. Composite Systems",
     "SS2026/Quantum Computing/5. Partial observing and measuring/Anhänge",
-    "SS2026/Quantum Computing/5. Partial observing and measuring",
     "SS2026/Quantum Computing/1. Introduction/Introduction to Quantum physics.md",
     "SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md",
     "SS2026/Quantum Computing/3. Quantum Systems/Quantum Systems.md",

SS2026/Quantum Computing/Bernstein-Vazirani/Bernstein-Vazirani Algorithm.md

@@ -2,4 +2,14 @@ The first quantum algorithm we will look at is the Bernstein-Vazirani algorithm.
 
 Given a secret s $\in \{0,1\}^n$ and the function f : $\{0,1\}^n \rightarrow \{0,1\}$ defined as f(x) = x * s
 \* denotes the inner product of two bitstrings here
-For Bitstrings x and y of length n the inner product x * y is 
+For Bitstrings x and y of length n the inner product x * y is $x_1y_1 + ... + x_ny_n$ mod 2
+The goal is to find the secret s using as few queries of f as possible.
+So as few evaluations of f as possible.
+
+We will look at a quantum algorithm that will find s with only one evaluation of f.
+
+![[Pasted image 20260730144713.png]]
+
+The top wire consists of n qubits in state 0.   $\ket{0}^n = \ket{0} \otimes ... \otimes \ket{0}$ 
+The bottom wire is in state 1.
+Both wires together are in state $\ket{0^n1} = \ket{0}^n \$