Quantum computing of delocalization in small-world networks

被引：39

作者：

Giraud, O ^{[1
]}

Georgeot, B ^{[1
]}

Shepelyansky, DL ^{[1
]}

机构：

[1] Univ Toulouse 3, CNRS, UMR 5152, Phys Theor Lab, F-31062 Toulouse, France

来源：

PHYSICAL REVIEW E | 2005年 / 72卷 / 03期

关键词：

D O I：

10.1103/PhysRevE.72.036203

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We study a quantum small-world network with disorder and show that the system exhibits a delocalization transition. A quantum algorithm is built up which simulates the evolution operator of the model in a polynomial number of gates for an exponential number of vertices in the network. The total computational gain is shown to depend on the parameters of the network and a larger than quadratic speedup can be reached. We also investigate the robustness of the algorithm in presence of imperfections.

引用

页数：4

共 20 条

[1] ELEMENTARY GATES FOR QUANTUM COMPUTATION [J].

BARENCO, A ;

BENNETT, CH ;

CLEVE, R ;

DIVINCENZO, DP ;

MARGOLUS, N ;

SHOR, P ;

SLEATOR, T ;

SMOLIN, JA ;

WEINFURTER, H .

PHYSICAL REVIEW A, 1995, 52 (05) :3457-3467

[2] Dynamical localization simulated on a few-qubit quantum computer [J].

Benenti, G ;

Casati, G ;

Montangero, S ;

Shepelyansky, DL .

PHYSICAL REVIEW A, 2003, 67 (05) :8

[3] A NUMERICAL STUDY OF SPARSE RANDOM MATRICES [J].

EVANGELOU, SN .

JOURNAL OF STATISTICAL PHYSICS, 1992, 69 (1-2) :361-383

[4] Quantum chaos and random matrix theory for fidelity decay in quantum computations with static imperfections [J].

Frahm, KM ;

Fleckinger, R ;

Shepelyansky, DL .

EUROPEAN PHYSICAL JOURNAL D, 2004, 29 (01) :139-155

[5] Emergence of quantum chaos in the quantum computes core and how to manage it [J].

Georgeot, B ;

Shepelyansky, DL .

PHYSICAL REVIEW E, 2000, 62 (05) :6366-6375

[6] Quantum chaos border for quantum computing [J].

Georgeot, B ;

Shepelyansky, DL .

PHYSICAL REVIEW E, 2000, 62 (03) :3504-3507

[7] Quantum mechanics helps in searching for a needle in a haystack [J].

Grover, LK .

PHYSICAL REVIEW LETTERS, 1997, 79 (02) :325-328

[8] Quantum and classical diffusion on small-world networks [J].

Kim, BJ ;

Hong, H ;

Choi, MY .

PHYSICAL REVIEW B, 2003, 68 (01)

[9] Chaotic scattering on graphs [J].

Kottos, T ;

Smilansky, U .

PHYSICAL REVIEW LETTERS, 2000, 85 (05) :968-971

[10] LOCALIZATION - THEORY AND EXPERIMENT [J].

KRAMER, B ;

MACKINNON, A .

REPORTS ON PROGRESS IN PHYSICS, 1993, 56 (12) :1469-1564

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