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