The Quantum States of a Graph

被引：0

作者：

Raza, Mohd Arif ^{[1
]}

Alahmadi, Adel N. ^{[2
]}

Basaffar, Widyan ^{[2
]}

Glynn, David G. ^{[3
]}

Gupta, Manish K. ^{[4
]}

Hirschfeld, James W. P. ^{[2
]}

Khan, Abdul Nadim ^{[1
]}

Shoaib, Hatoon ^{[2
]}

Sole, Patrick ^{[5
]}

机构：

[1] King Abdulaziz Univ, Fac Sci & Arts Rabigh, Dept Math, Res Grp Algebra Struct & Applicat, Rabigh 21911, Saudi Arabia

[2] King Abdulaziz Univ, Fac Sci, Dept Math, Res Grp Algebra Struct & Applicat, Jeddah 21589, Saudi Arabia

[3] Flinders Univ S Australia, Coll Sci & Engn, Adelaide, SA 5001, Australia

[4] Dhirubhai Ambani Inst Informat & Commun Technol, Gandhinagar 382007, Gujarat, India

[5] Aix Marseille Univ, CNRS, Cent Marseille, I2M, 163 Ave Luminy, F-13009 Marseilles, France

来源：

MATHEMATICS | 2023年 / 11卷 / 10期

关键词：

quantum state; graph; self-dual quantum code; Eulerian graph;

D O I：

10.3390/math11102310

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Quantum codes are crucial building blocks of quantum computers. With a self-dual quantum code is attached, canonically, a unique stabilised quantum state. Improving on a previous publication, we show how to determine the coefficients on the basis of kets in these states. Two important ingredients of the proof are algebraic graph theory and quadratic forms. The Arf invariant, in particular, plays a significant role.

引用

页数：13

共 50 条

[1] Quantum secret sharing with quantum graph states
Liang Jian-Wu
Cheng Zi
Shi Jin-Jing
Guo Ying
[J]. ACTA PHYSICA SINICA, 2016, 65 (16)
[2] Growth of graph states in quantum networks
Cuquet, Marti
Calsamiglia, John
[J]. PHYSICAL REVIEW A, 2012, 86 (04)
[3] Graph States as a Resource for Quantum Metrology
Shettell, Nathan
Markham, Damian
[J]. PHYSICAL REVIEW LETTERS, 2020, 124 (11)
[4] BDD Operations for Quantum Graph States
Hiraishi, Hidefumi
Imai, Hiroshi
[J]. REVERSIBLE COMPUTATION, RC 2014, 2014, 8507 : 216 - 229
[5] Graph states for quantum secret sharing
Markham, Damian
Sanders, Barry C.
[J]. PHYSICAL REVIEW A, 2008, 78 (04):
[6] Quantum Lego: Graph States for Quantum Computing and Information Processing
Markham, Damian
[J]. ERCIM NEWS, 2018, (112): : 19 - 19
[7] Graph coherent states for loop quantum gravity
Assanioussi, Mehdi
[J]. PHYSICAL REVIEW D, 2020, 101 (12):
[8] Distributing Graph States Across Quantum Networks
Fischer, Alex
Towsley, Don
[J]. 2021 IEEE INTERNATIONAL CONFERENCE ON QUANTUM COMPUTING AND ENGINEERING (QCE 2021) / QUANTUM WEEK 2021, 2021, : 324 - 333
[9] Efficient generation of graph states for quantum computation
Clark, SR
Alves, CM
Jaksch, D
[J]. NEW JOURNAL OF PHYSICS, 2005, 7
[10] Entanglement and separability of graph Laplacian quantum states
Joshi, Anoopa
Singh, Parvinder
Kumar, Atul
[J]. QUANTUM INFORMATION PROCESSING, 2022, 21 (04)

← 1 2 3 4 5 →