Hidden shift problem
The Hidden shift problem states: Given an oracle formula_1 that encodes two functions formula_2 and formula_3, there is an n-bit string formula_4 for which formula_5 for all formula_6. Find formula_4. Many functions, such as the Legendre symbol and Bent functions, satisfy these constraints. With a quantum algorithm that's defined as "formula_8" where formula_9 is the Hadamard gate and formula_10 is the fourier transform of formula_3, this problem can be solved in a polynomial number of queries to formula_12 while taking exponential queries with a classical algorithm. The difference between the Hidden subgroup problem and the Hidden shift problem is that the former focuses on the underlying group while the later focuses on the underlying ring or field.
Q1143357
oracle
Concept
Q748339
Legendre symbol
Concept
Q4890350
Bent functions
UNK
Q2623817
quantum algorithm
Concept
Q1014065
Hadamard gate
UNK
Q6520159
fourier transform
Concept
Q5752087
Hidden subgroup problem
UNK
Q83478
group
Concept
Q161172
ring
Concept
Q190109
field
Concept
Q96381001
Hidden shift problem
UNK
Q96381001
Hidden shift problem
UNK
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subclass of