منابع مشابه
Continuous Quantum Hidden Subgroup Algorithms
In this paper we show how to construct two continuous variable and one continuous functional quantum hidden subgroup (QHS) algorithms. These are respectively quantum algorithms on the additive group of reals R, the additive group R/Z of the reals Rmod 1, i.e., the circle, and the additive group Paths of L paths x : [0, 1] → R in real n-space R. Also included is a curious discrete QHS algorithm ...
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One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the Deutsch-Jozsa, Simon, Shor algorithms, and many more. In this paper, our strategy for finding new quantum algorithms is to decompose Shor’s quantum factoring algorithm...
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In a series of works [18, 21, 19, 20, 23, 22], Geiß-Leclerc-Schröer defined the cluster algebra structure on the coordinate ring C[N(w)] of the unipotent subgroup, associated with a Weyl group element w. And they proved cluster monomials are contained in Lusztig’s dual semicanonical basis S∗. We give a set up for the quantization of their results and propose a conjecture which relates the quant...
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We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carrylookahead (qcla) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary qubits. We present both in-place and out-of-place versions, as well as versions that add modulo 2n and modulo 2n − 1. Previously, the linear-depth ripple-carry ...
متن کاملThe Hidden Subgroup Problem and EigenvalueEstimation on a Quantum
A quantum computer can eeciently nd the order of an element in a group, factors of composite integers, discrete logarithms, sta-bilisers in Abelian groups, and hidden or unknown subgroups of Abelian groups. It is already known how to phrase the rst four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the solution to the more general Abelian hidden subgro...
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ژورنال
عنوان ژورنال: Acta Mathematica Hungarica
سال: 2017
ISSN: 0236-5294,1588-2632
DOI: 10.1007/s10474-017-0694-6