15
o '£t29vEEFfz⇒iFuFItH¥¥ ) Bosousamptf Aaronson Hadanard Test Iap - Arkhipoiaj irate 's "H÷¥¥¥hE:d ; ¥÷#=1 . EEK.dk#EEnl?=*rEokI 2 DQCT ( one - deanqabtemodel ) kill Laflamme . PRL '98 Tones '72kFa2GHh . Shor Jordan Quarter Into . & Comp . Hardness atop cof . Morine Fuji - Fitzsimons PRL94 Fujii etal ICALP 96 GnXiv95 ) 10>-0+12-67 vk.IQ#FEEt3EsEf , Aharonovetal arXivc05

1 H÷¥¥¥hE:d '£t29vEEFfz⇒iFuFItH¥¥ EEK.dk#EEnl?=*rEokI · 2020. 5. 13. · Part ZFEFEEYZJE e-fIzaEt¥EtF p → p '= ECP) t' FEE9571 rafter = CPTPITBA completely post't 've

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  • o

    '£t29vEEFfz⇒iFuFItH¥¥

    )Bosousamptf

    AaronsonHadanard Test

    . Iap - Arkhipoiaj

    irate 's "H÷¥¥¥hE:d;¥÷#=1.EEK.dk#EEnl?=*rEokI2

    DQCT ( one - deanqabtemodel )

    kill - Laflamme.

    PRL '98

    Tones '72kFa2GHh.

    Shor . Jordan Quarter Into . & Comp .

    Hardness atop cof .

    Morine - Fuji - Fitzsimons PRL94Fujii etal ICALP 96 GnXiv95 )

    10>-0+12-67

    vk.IQ#FEEt3EsEf ,Aharonovetal arXivc05

  • lsttt) = fate" " Ylxiscxil

    ÷ ( I - o ) = { ( I - e⇐" "

    ) lxixxil

    E

    P → &E+⇒pc←o5rhEHpC⇐⇒+

    axejscijlxisciylECp£=#y¢ke⇐imja+e#'s )+4 - ed 's Ct Ee ' " ) }{ ( ffix ) = Pfix £ ' ) .

    as Icy ( ie⇐"" ' → ' )

    Itf At a"

    di F Xj EGZE .

    Cy to as' ri Ts ) .

    Pfk 12 II Kaila IEEE .→ Hadamard test 2

    " Eti × "

    at THEE eaiazyhikxiHad "↳ ' "LKFKBZ , '

  • Part ZFEFEEYZJE.

    e - fIzaEt¥EtF .

    p → p'= ECP )

    t'

    FEE9571 rafter,

    = CPTPITBAcompletely post't 've

    *positive trace presents.

    P '= ECP ) 30

    acompletenessEQIsfao ) do•Trcqp ) )=1 .

    CPTP a Kraus Efte

    Ecp )=IaEapEI .

  • o Fatrvh .F-

    QHDT.EE#k.ctfizausEiFsEA'ek

    .

    %"

    µµ+pM )1¥,

    £¥*? inotisinozoz

    = =p#e¥d→¥→.ie#reee

    '

    I 'v7=7" c UJZ,

    rIrEatTEaiLnETtEn5bu-sreduceddenstymatrlxKtloXoHasF@7oxrtEplnxoDtiMtDalbTtxagn.iaxas.l

    rata

    ECP ) = ftp.#ozp aF9k¥ ¥2 " iibilzaitfta 73 .

  • o ¥23112"

    capsize. ECP ) - Ea ,EaPEI

    \Kraus Fahd

    .

    ( [k#tiI ← Tree pD=TrG¥a$An ) 107 → EFEKPEMDYXETFR .

    4-ptkolt p11741

    Excp )= ctpp +1¥E '→fQ¥Eh} -

    Ez (p ) = Ctp ) PtpzpztkF#E#Z[ 3-

    .Kennett's":$YkikFyE¥£7 kziet 'll .

  • XP

    -1Pakilo>aHcnF&p*pal+x*pnxoDtiMtD4fzet latloxoltlethkrl -ECP )='ftp.#ozp2

    F9k¥ ¥2 " iiD4Zaikk#R3 ,

  • bBtflF.yZT3EdshorJqnETIeeeIYFIk.ua.iFighteutaugtementwHreueaybnendlbyPreskl4Llo7tptD-L1ooo7tP111DAh-zoIo-sA0td1ooo3lmn72yIREyfzhEsR.zRzIpbEPrDn5BTtcodespace@I3-l.FEftIFoEee.imnesHraorliomsMximooaEFEk5yk10717077xx.x3diytkEhI5-aiEE4h3EEkRa99En.S

    totalizer

    ZZZ ,ZR}a#FtEE' RYHEEFRPpg .tt#.EtTBweTikI5fEDZ .

  • a 2745441454'

    ( Gottesman'

    97 )

    zyEk#B4 /an

    o.GEft NDYETL , fcftttigxthkqz }. 'S ; ,§Ef ,[Si , 570 . FFFE .•

    - Zeff ETAKE . 'Ll .HE '5h'THiYv

    S , IE > = IE > foray C .

    either '¥tlE7

    (1/311) { 5×1×2,72+-4.424=4'xixyZkDEFXE .→ ( 100>+1717)fE

  • ostqubkcode

    .gJEEacibYFkY39

    s ,=z××zTt.DE#EEeoHtiH..zFg '

    '

    Sz - [ ZXXZ

    s}=zIzx× f1&7=/E > forallt

    S¢= XZTZX FI ' ftp.zakfz#iF43 ,

    2%4=2*04

    "*H¥.a¥µ=÷tI!t¥¥*EIE÷*⇐**EY¥÷fEEK SNSL ,

    EFFFF.

    HDSKFT )

    → S :(EIED :(EIED Pastawskifetal

    't

    S~S¢{ Kiss ,steal

    " subspace ^ .

    Lato7=157,↳lT7=tMLxlzz - Lz↳t 's LXIJ7=1 I >

    No >+ph > → XIJ >t BIT >

  • / J >=¥( 000007+1100107+101001>+401007+1010107-1110117-1001107-111000)

    -1111017-1000117-111110>-1011117

    -1100017-101100>-1101117+1001013{Etf±n- f- vacant ! !

    o YIFEZEZKNKI ( code distance )

    D= mywt C L )

    logicaloperated 5£21 - AD 'HEIt5Q

    .

    ↳ = X*5 KK ) wtltexzoy= 2

    .

    ↳ Sa = TTIY × wtkxs , ) =3,

    theological operator

    Fqubte code D code ¥1

  • TYTFEEZHIE

    '=¥Fs#BER¥oFs÷¥4 ,

    as -% le 's=xio7ta¥¥3-/ ' daifatofkN54IEs¥itebbh¥#Htz

    .

    €n¥fFER⇒9Isi 'B2EZ

    .

    d=3 → loose '7e£5IE.

    EREEIYHIAEEERERGBSY .Y 6iBtaIst" oh .

    Fnqubkahx .AZ#bfkCx.4.z)a23-3×5=15

    15+1=16 .⇒ - kssfixa

    ⇒⇒uailH1£Tw

    .

    S ,~S -49172154 .EE#24YiE55E.

    X , → ( +1 .tl , -1 ,tl ) Kph '¥Pi8Ekk°BY

    Zy→ Ctbtl , -1 , -1 ) F¥tBixI7*¥cT( YK )→C⇒HH , -1 ) Ocpz )

  • oIzaEbEYFt5eFtzH4ZECpHIEfEgkGftz3EyH.gpyegeEzersPE5tdu.HFZa3EaAlEXElAIalExeItEp.x.Y.Zlp9BitEiiEiRcps-5gRePRetEIa2.ReAlE7x1ey.aEBatnzu3@R.E

    a#a=?Eat Cit CIX+C!Y+c£z

    Re Ehle 7 X le >stalk .

    R.EC#ehEeEReErfkIRe=khEI

  • t :#Faith