Classical simulation of quantum many-body systems with a tree tensor network

被引：410

作者：

Shi, Y. -Y. ^{[1
]}

Duan, L. -M.

Vidal, G.

机构：

[1] Univ Michigan, Dept Elect Engn & Comp Sci, Ann Arbor, MI 48109 USA

[2] Univ Michigan, FOCUS Ctr, Ann Arbor, MI 48109 USA

[3] Univ Michigan, Dept Phys, MCTP, Ann Arbor, MI 48109 USA

[4] Univ Queensland, Sch Phys Sci, St Lucia, Qld 4072, Australia

来源：

PHYSICAL REVIEW A | 2006年 / 74卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1103/PhysRevA.74.022320

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

引用

页数：4

共 32 条

[1] Improved simulation of stabilizer circuits [J].

Aaronson, S ;

Gottesman, D .

PHYSICAL REVIEW A, 2004, 70 (05) :052328-1

[2] VALENCE BOND GROUND-STATES IN ISOTROPIC QUANTUM ANTIFERROMAGNETS [J].

AFFLECK, I ;

KENNEDY, T ;

LIEB, EH ;

TASAKI, H .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 115 (03) :477-528

[3] Persistent entanglement in arrays of interacting particles [J].

Briegel, HJ ;

Raussendorf, R .

PHYSICAL REVIEW LETTERS, 2001, 86 (05) :910-913

[4] Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces -: art. no. P04005 [J].

Daley, AJ ;

Kollath, C ;

Schollwöck, U ;

Vidal, G .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2004,

[5] FINITELY CORRELATED STATES ON QUANTUM SPIN CHAINS [J].

FANNES, M ;

NACHTERGAELE, B ;

WERNER, RF .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 144 (03) :443-490

[6] GROUND-STATES OF VBS MODELS ON CAYLEY TREES [J].

FANNES, M ;

NACHTERGAELE, B ;

WERNER, RF .

JOURNAL OF STATISTICAL PHYSICS, 1992, 66 (3-4) :939-973

[7] A density matrix renormalization group approach to interacting quantum systems on Cayley trees [J].

Friedman, B .

JOURNAL OF PHYSICS-CONDENSED MATTER, 1997, 9 (42) :9021-9029

[8]

GOTTESMAN D, QUANTPH9807006

[9]

GREEN SFF, QUANTPH0312209

[10] Numerical renormalization approach to two-dimensional quantum antiferromagnets with valence-bond-solid type ground state [J].

Hieida, Yasuhiro ;

Okunishi, Kouichi ;

Akutsu, Yasuhiro .

NEW JOURNAL OF PHYSICS, 1999, 1 :7.1-7.17

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