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Quantum circuits and quantum algorithms.

Zhang, Yong.

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Quantum circuits and quantum algorithms.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quantum circuits and quantum algorithms./
作者:	Zhang, Yong.
面頁冊數:	77 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-07, Section: B, page: 3814.
Contained By:	Dissertation Abstracts International66-07B.
標題:	Computer Science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3182004
ISBN:	9780542223549

Quantum circuits and quantum algorithms.
Zhang, Yong.

Quantum circuits and quantum algorithms. - 77 p.

Source: Dissertation Abstracts International, Volume: 66-07, Section: B, page: 3814.

Thesis (Ph.D.)--University of South Carolina, 2005.

In the dissertation we study topics in quantum computation. First, we study the model of constant-depth quantum circuits. We study the family QNC0 of constant-depth quantum circuits, and the complexity classes associated with QNC0 circuits: EQNC0, NQNC0, and BQNC0e,d . We show certain containment results such as NQNC 0 = NQACC = NQP = coC =P and BQNC0e,d is in P for certain epsilon and delta. Our results essentially refute a conjecture of Green et al. that NQACC &sube; TC0. We also define and study complexity classes postEQP, postRQP, postNQP, and postBQNC0 We show containment results such as postBQNC0 = postBQP = PP and NQP = postRQP = postNQP.

ISBN: 9780542223549Subjects--Topical Terms:

626642
Computer Science.

Quantum circuits and quantum algorithms.
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500 $a Source: Dissertation Abstracts International, Volume: 66-07, Section: B, page: 3814.
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502 $a Thesis (Ph.D.)--University of South Carolina, 2005.
520 $a In the dissertation we study topics in quantum computation. First, we study the model of constant-depth quantum circuits. We study the family QNC0 of constant-depth quantum circuits, and the complexity classes associated with QNC0 circuits: EQNC0, NQNC0, and BQNC0e,d . We show certain containment results such as NQNC 0 = NQACC = NQP = coC =P and BQNC0e,d is in P for certain epsilon and delta. Our results essentially refute a conjecture of Green et al. that NQACC &sube; TC0. We also define and study complexity classes postEQP, postRQP, postNQP, and postBQNC0 We show containment results such as postBQNC0 = postBQP = PP and NQP = postRQP = postNQP.
520 $a Second, we study applications of quantum algorithms in computational group theory. We give results about quantum algorithms and reductions for group theoretic problems, concentrating mostly on solvable groups. We study two particular group theoretic problems---GROUP I NTERSECTION and DOUBLE COSET M EMBERSHIP. We show that these problems reduce to other group problems with known efficient quantum algorithms for many instances, yielding efficient quantum algorithms for GROUP INTERSECTION and DOUBLE COSET MEMBERSHIP on the same types of groups. Then we generalize and refine our results by introducing decision versions of the STABILIZER and ORBIT COSET problems, and showing that these new problems lie in between GROUP INTERSECTION and DOUBLE COSET MEMBERSHIP on the one hand, and the problem ORBIT SUPERPOSITION, on the other. We also show that GROUP INTERSECTION and D OUBLE COSET MEMBERSHIP have statistical zero knowledge proofs. Finally we give an alternative quantum algorithm for the problem of decomposing finite abelian groups.
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