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Quantum algorithms for testing Boolean functions
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for
finding which variables a Boolean function depends on. There are 2^n possible
linear Boolean functions of n variables; given a linear Boolean function, the
Bernstein-Vazirani quantum algorithm can deterministically identify which one
of these Boolean functions we are given using just one single function query.
The same quantum algorithm can also be used to learn which input variables
other types of Boolean functions depend on, with a success probability that
depends on the form of the Boolean function that is tested, but does not depend
on the total number of input variables. We also outline a procedure to futher
amplify the success probability, based on another quantum algorithm, the Grover
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