Bernstein–Vazirani Algorithm
The Bernstein–Vazirani algorithm, which solves the Bernstein–Vazirani problem, is a quantum algorithm invented by Ethan Bernstein and Umesh Vazirani in 1997. It is a restricted version of the Deutsch–Jozsa algorithm where instead of distinguishing between two different classes of functions, it tries to learn a string encoded in a function. The Bernstein–Vazirani algorithm was designed to prove an oracle separation between Complexity class, complexity classes BQP and BPP (complexity), BPP. Problem statement Given an Oracle machine, oracle that implements a function f\colon\^n\rightarrow \ in which f(x) is promise problem, promised to be the dot product between x and a secret string s \in \^n Modular arithmetic, modulo 2, f(x) = x \cdot s = x_1s_1 \oplus x_2s_2 \oplus \cdots \oplus x_ns_n, find s. Algorithm Classically, the most efficient method to find the secret string is by evaluating the function n times with the input values x = 2^ for all i \in \: : \be ...
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