On Quantum Algorithms for Noncommutative Hidden Subgroups

Stability of additive functional equation on discrete quantum semigroups

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

Limitations of single coset states and quantum algorithms for code equivalence

Quantum computers can break the RSA, El Gamal, and elliptic curve public-key cryptosystems, as they can efficiently factor integers and extract discrete logarithms. The power of such quantum attacks lies in quantum Fourier sampling, an algorithmic paradigm based on generating and measuring coset states. In this article we extend previous negative results of quantum Fourier sampling for Graph Is...

Quantum Algorithms For Hidden Subgroups Of Sn

ar X iv : q ua nt - p h / 02 11 09 1 v 1 1 5 N ov 2 00 2 Hidden Translation and Orbit Coset in Quantum Computing ∗

We give efficient quantum algorithms for HIDDEN TRANSLATION and HIDDEN SUBGROUP in a large class of non-abelian groups including solvable groups of bounded exponent and of bounded derived series. Our algorithms are recursive. For the base case, we solve efficiently HIDDEN TRANSLATION in Z p , whenever p is a fixed prime. For the induction step, we introduce the problem ORBIT COSET generalizing ...

On some possible mathematical connections concerning Noncommutative Minisuperspace Cosmology, Noncommutative Quantum Cosmology in low-energy String Action, Noncommutative Kantowsky-Sachs Quantum Model, Spectral Action Principle associated with a Noncommutative Space and some aspects concerning the Loop Quantum Gravity

This paper is a review of some interesting results that has been obtained in various sectors of noncommutative cosmology, string theory and loop quantum gravity. In the Section 1, we have described some results concerning the noncommutative model of the closed Universe with the scalar field. In the Section 2, we have described some results concerning the low-energy string effective quantum cosm...