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The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring , discrete logarithm , graph isomorphism , and the shortest vector problem .
The discrete logarithm algorithm and the factoring algorithm are instances of the period-finding algorithm, and all three are instances of the hidden subgroup problem. On a quantum computer, to factor an integer N {\displaystyle N} , Shor's algorithm runs in polynomial time , meaning the time taken is polynomial in log N {\displaystyle \log ...
Simon's problem considers access to a function : {,} {,}, as implemented by a black box or an oracle. This function is promised to be either a one-to-one function, or a two-to-one function; if is two-to-one, it is furthermore promised that two inputs and ′ evaluate to the same value if and only if and ′ differ in a fixed set of bits. I.e.,
The abelian hidden subgroup problem is a generalization of many problems that can be solved by a quantum computer, such as Simon's problem, solving Pell's equation, testing the principal ideal of a ring R and factoring. There are efficient quantum algorithms known for the Abelian hidden subgroup problem. [10]
Hidden linear function problem; Hidden shift problem; Hidden subgroup problem; P. Path integral Monte Carlo; Q. HHL algorithm; Quantum annealing; Quantum artificial life;
Heyde theorem-- Heyting algebra-- Heyting arithmetic-- Heyting field-- Hicks equation-- Hicksian demand function-- Hidato-- Hidden algebra-- Hidden attractor-- Hidden Field Equations-- Hidden Figures (book)-- Hidden linear function problem-- Hidden Markov model-- Hidden Markov random field-- Hidden semi-Markov model-- Hidden subgroup problem ...
Like the rest of your body, your brain requires optimal nutrition to function at its best. Vitamins, antioxidants, isoflavones, omega-3 fats and carotenoids have all been shown to promote better ...
A core-free subgroup is a subgroup whose normal core is the trivial subgroup. Equivalently, it is a subgroup that occurs as the isotropy subgroup of a transitive, faithful group action. The solution for the hidden subgroup problem in the abelian case generalizes to finding the normal core in case of subgroups of arbitrary groups.