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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 .
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 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 ...
Himmelblau's function-- Hindley–Milner type system-- Hindmarsh–Rose model-- Hindu–Arabic numeral system-- Hindu units of time-- Hindustani numerals-- Hinge theorem-- Hinged dissection-- Hippopede-- Hiptmair–Xu preconditioner-- Hironaka decomposition-- Hironaka's example-- Hiroshima Mathematical Journal-- Hiroyuki Goto-- Hirsch ...
The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 1996 by the theoretical physicist David P. DiVincenzo, [1] as being those necessary to construct such a computer—a computer first proposed by mathematician Yuri Manin, in 1980, [2] and physicist Richard Feynman, in 1982 [3] —as a means to efficiently simulate quantum systems, such ...
The representative functions A form a non-commutative algebra under convolution with respect to Haar measure μ. The analogue for a finite subgroup of Γ of SU(2) is the finite-dimensional group algebra C[Γ] From the Clebsch-Gordan rules, the convolution algebra A is isomorphic to a direct sum of n × n matrices, with n = 2j + 1 and j ≥ 0.
Let G be a compact, connected Lie group and let be the Lie algebra of G.The first main result is the torus theorem, which may be formulated as follows: [2] Torus theorem: If T is one fixed maximal torus in G, then every element of G is conjugate to an element of T.
This list contains quantum processors, also known as quantum processing units (QPUs).Some devices listed below have only been announced at press conferences so far, with no actual demonstrations or scientific publications characterizing the performance.