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