Distribution of G-concurrence of random pure states

The Institute of Electrical and Electronics Engineers, Inc.345 East 47th Street, New York, NY 10017-2394, USA

Copyright © 1997 by the Institute of Electrical and Electronics Engineers, Inc.All rights reserved. Published 1997. Printed in the United States of America.

ISBN 1-55937-937-5

No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher.

IEEE Std 1243-1997

IEEE Guide for Improving the

Lightning Performance of

Transmission Lines

Sponsor

Transmission and Distribution Committee

of the

IEEE Power Engineering Society

Approved 26 June 1997

IEEE Standards Board

Abstract:

The effects of routing, structure type, insulation, shielding, and grounding on transmis-

sion lines are discussed. The way these transmission-line choices will improve or degrade light-

2020，56（8）

1引言作为一种新颖的计算模型，量子计算具有两个突出的特点：其一量子态的叠加和纠缠等性质可以完成并行计算处理加快数据的计算速率，具有代表性的是肖尔（Shor）大数分解算法[1]、波色取样[2]、格罗夫尔（Grover）搜索[3]、量子退火算法等。其二n个量子比特有2n个状态即n个量子比特可以存储2n位信息，提高了信息存储空间，例如运用在量子图像处理中，量子图像表示（QIMR）起着关键的作用[4-8]。卷积神经网络在数据信息处理方面有助于改进机器学习，例如在物体分类[9-13]、目标检测[14-16]等领域已取得不错成就。随着社会的发展，卷积神经网络的计算数据愈加庞大，导致计算速率愈加缓慢，量子计算相比于经典计算具有更高的优势[17-18]，因此需要借用量子计算的原理或概念计算卷积，以提高卷积神经网络计算速率。许兴阳、刘宏志[19]通过给出卷积算术线路定义，进而设计出了量子门组卷积神经网络模型（QGCNN）；CongI等[20]引入并分析了受机器学习启发的量子线路模型QuantumConvolutionalNeuralNetworks（QCNN），证明了QCNN可以准确识别与一维对称保护拓扑阶段相关的量子状态及对给定的未知错误模型优化的量子错误校正方案，其性能优于现有方法；HendersonM一维量子卷积计算

闫茜茜，王鹏程，刘兴云湖北师范大学物理与电子科学学院，湖北黄石435002

摘要：研究了一维信息编码为量子态后进行量子卷积计算的量子线路模型。基于量子图像表示和经典信息的卷积算法，设计出了一维量子卷积计算的量子线路结构，表明量子卷积计算可以以O(n2)的复杂度计算卷积。与经典

卷积相比，量子卷积计算由于利用量子并行计算在计算速率上达到了指数级的加速，为量子卷积神经网络卷积层的设计实施作铺垫。关键词：量子门；卷积计算；量子线路文献标志码：A中图分类号：TP18doi：10.3778/j.issn.1002-8331.1911-0097

Thepurposeofthislectureistodiscussaselectionofexamplesofstates,measurements,andoper-

ations.Wewillseesomeoftheseexamplesabitlaterinthecourse,andthelastone(teleportation)

isveryimportantinquantuminformationtheory.Youshould,however,notreadtoomuchinto

theparticularselectionofexamplesinthislecture—itisconvenienttodiscusstheseexamplesnow,

forthesakeoflecturescomingup,butthereareofcoursemanyimportantexamplesthatwewill

notdiscussatthepresenttime.

6.1Convexcombinationsofstates,measurements,andoperations

Iassumethatyouarefamiliarwithconvexityandthebasicnotionsthatconcernit.Recallthat

asubsetC⊆V

ofsomevectorspaceV

isconvexif,forallchoicesofx,y∈C

andλ∈[

0,1]

,it

holdsthatλx+(

1−

λ)

y∈C

.Whenwerefertoaconvexcombinationofelementsfromsomesubset

A⊆V

ofavectorspaceV

,wearereferringtoa(finite)linearcombinationoftheform

N

∑

j=1p

jx

j,

wherex

1,...,x

DetrimentalDecoherence

GilKalai∗

HebrewUniversityofJerusalemandYaleUniversity

November23,2007

Abstract

Weproposeanddiscusstwoconjecturesonthenatureofinforma-tionleaks(decoherence)forquantumcomputers.Theseconjectures,if(orwhen)theyhold,aredamagingforquantumerror-correctionasrequiredbyfault-tolerantquantumcomputation.Thefirstconjectureassertsthatinformationleaksforapairofsubstantiallyentangledqubitsarethemselvessubstantiallypositivelycorrelated.Thesecondconjectureassertsthatinanoisyquantumcomputerwithhighlyentangledqubitstherewillbeastrongeffectoferrorsynchronization.Wepresentamoregeneralconjectureforarbitrarynoisyquantumsystems:prescribing(ordescribing)noisyquantumsystemsatastateρissubjecttoerrorEwhich“tendstocommute”witheveryunitaryoperatorthatstabilizesρ.1Quantumcomputersandthethresholdthe-

orem

Quantumcomputersarehypotheticaldevicesbasedonquantumphysics.A