<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-01490947v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-16T02:15:43+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Interpolation Methods for Binary and Multivalued Logical Quantum Gate Synthesis</title>
            <author role="aut">
              <persName>
                <forename type="first">Zeno</forename>
                <surname>Toffano</surname>
              </persName>
              <email type="md5">7226159b4eeffb00c3c4ca7dd32e6715</email>
              <email type="domain">centralesupelec.fr</email>
              <idno type="idhal" notation="string">ztoffano</idno>
              <idno type="idhal" notation="numeric">11258</idno>
              <idno type="halauthorid" notation="string">32186-11258</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-8594-3291</idno>
              <idno type="IDREF">https://www.idref.fr/058926496</idno>
              <affiliation ref="#struct-411575"/>
              <affiliation ref="#struct-1289"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">François</forename>
                <surname>Dubois</surname>
              </persName>
              <email type="md5">7100fbdba619da95bd78e41602d38c79</email>
              <email type="domain">math.u-psud.fr</email>
              <idno type="idhal" notation="string">francois-dubois</idno>
              <idno type="idhal" notation="numeric">1237807</idno>
              <idno type="halauthorid" notation="string">166287-1237807</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4858-6234</idno>
              <affiliation ref="#struct-85486"/>
              <affiliation ref="#struct-12568"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Zeno</forename>
                <surname>Toffano</surname>
              </persName>
              <email type="md5">7226159b4eeffb00c3c4ca7dd32e6715</email>
              <email type="domain">centralesupelec.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2017-03-20 17:40:32</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2017-05-08 15:55:23</date>
              <date type="whenWritten">2017-03-10</date>
              <date type="whenModified">2026-01-29 17:41:23</date>
              <date type="whenReleased">2017-05-17 11:25:13</date>
              <date type="whenProduced">2017-06-14</date>
              <date type="whenEndEmbargoed">2017-05-08</date>
              <ref type="file" target="https://centralesupelec.hal.science/hal-01490947v2/document">
                <date notBefore="2017-05-08"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://centralesupelec.hal.science/hal-01490947v2/file/TCQ-2017-Z_Z.pdf" id="file-1519563-1580629">
                <date notBefore="2017-05-08"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="446548">
                <persName>
                  <forename>Zeno</forename>
                  <surname>Toffano</surname>
                </persName>
                <email type="md5">7226159b4eeffb00c3c4ca7dd32e6715</email>
                <email type="domain">centralesupelec.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01490947</idno>
            <idno type="halUri">https://centralesupelec.hal.science/hal-01490947</idno>
            <idno type="halBibtex">toffano:hal-01490947</idno>
            <idno type="halRefHtml">&lt;i&gt;TQC2017 - Theory of Quantum Computation, Communication and Cryptography&lt;/i&gt;, UPMC, Jun 2017, Paris, France</idno>
            <idno type="halRef">TQC2017 - Theory of Quantum Computation, Communication and Cryptography, UPMC, Jun 2017, Paris, France</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1519563-1580629"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-PSUD">Université Paris Sud - Paris XI</idno>
            <idno type="stamp" n="CNAM">Conservatoire National des Arts et Métiers</idno>
            <idno type="stamp" n="SUP_LSS">Laboratoire des Signaux et Systèmes</idno>
            <idno type="stamp" n="SUP_TELECOMS" corresp="SUP_LSS">Pôle Télécoms et Réseaux</idno>
            <idno type="stamp" n="CENTRALESUPELEC">Ecole CentraleSupélec</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIV-PSUD-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris Sud pour Paris Saclay</idno>
            <idno type="stamp" n="CENTRALESUPELEC-SACLAY" corresp="UNIV-PARIS-SACLAY">CENTRALESUPELEC-SACLAY</idno>
            <idno type="stamp" n="LMSSC-CNAM" corresp="CNAM">Laboratoire de mécanique des structures et des systèmes couplés</idno>
            <idno type="stamp" n="GS-ENGINEERING">Graduate School Sciences de l'Ingénierie et des Systèmes</idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="TEST3-HALCNRS">TEST3-HALCNRS</idno>
            <idno type="stamp" n="HESAM-CNAM" corresp="HESAM">Conservatoire National des Arts et Métiers - Hesam</idno>
            <idno type="stamp" n="HESAM">Hesam</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="0">No</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Interpolation Methods for Binary and Multivalued Logical Quantum Gate Synthesis</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Zeno</forename>
                    <surname>Toffano</surname>
                  </persName>
                  <email type="md5">7226159b4eeffb00c3c4ca7dd32e6715</email>
                  <email type="domain">centralesupelec.fr</email>
                  <idno type="idhal" notation="string">ztoffano</idno>
                  <idno type="idhal" notation="numeric">11258</idno>
                  <idno type="halauthorid" notation="string">32186-11258</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-8594-3291</idno>
                  <idno type="IDREF">https://www.idref.fr/058926496</idno>
                  <affiliation ref="#struct-411575"/>
                  <affiliation ref="#struct-1289"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">François</forename>
                    <surname>Dubois</surname>
                  </persName>
                  <email type="md5">7100fbdba619da95bd78e41602d38c79</email>
                  <email type="domain">math.u-psud.fr</email>
                  <idno type="idhal" notation="string">francois-dubois</idno>
                  <idno type="idhal" notation="numeric">1237807</idno>
                  <idno type="halauthorid" notation="string">166287-1237807</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4858-6234</idno>
                  <affiliation ref="#struct-85486"/>
                  <affiliation ref="#struct-12568"/>
                </author>
              </analytic>
              <monogr>
                <meeting>
                  <title>TQC2017 - Theory of Quantum Computation, Communication and Cryptography</title>
                  <date type="start">2017-06-14</date>
                  <date type="end">2017-06-16</date>
                  <settlement>Paris</settlement>
                  <country key="FR">France</country>
                </meeting>
                <respStmt>
                  <resp>conferenceOrganizer</resp>
                  <name>UPMC</name>
                </respStmt>
                <imprint/>
              </monogr>
              <ref type="publisher">http://tqc2017.lip6.fr/</ref>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">interpolation</term>
                <term xml:lang="en">linear algebra</term>
                <term xml:lang="en">quantum gates</term>
                <term xml:lang="en">Boolean functions</term>
                <term xml:lang="en">quantum angular momentum</term>
                <term xml:lang="en">multivalued logic</term>
              </keywords>
              <classCode scheme="halDomain" n="phys.qphy">Physics [physics]/Quantum Physics [quant-ph]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a family of logical operators corresponding to the one-argument logical connectives. Scaling up to n-arity gates is obtained by using the Kronecker product and unitary transformations. The quantum version of the Fourier transform of Boolean function is presented and a method for Reed-Muller decomposition is derived. The common control gates can be easily obtained by considering the logical correspondence between the control logic operator and the binary logic operator. A new polynomial and exponential formulation of the Toffoli gate is presented. The method has parallels to quantum gate-T optimization methods using powers of multilinear operator polynomials. The method is then applied naturally to alphabets greater than two for multi-valued logical gates used for quantum Fourier transform, min-max decision circuits and multivalued adders.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-411575" status="VALID">
          <idno type="IdRef">184443237</idno>
          <idno type="ROR">https://ror.org/019tcpt25</idno>
          <orgName>CentraleSupélec</orgName>
          <desc>
            <address>
              <addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.centralesupelec.fr</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1289" status="OLD">
          <idno type="IdRef">133818799</idno>
          <idno type="RNSR">199812842X</idno>
          <orgName>Laboratoire des signaux et systèmes</orgName>
          <orgName type="acronym">L2S</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.l2s.centralesupelec.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92966" type="direct"/>
            <relation active="#struct-411575" type="direct"/>
            <relation name="UMR8506" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-85486" status="OLD">
          <orgName>Université Paris-Sud - Paris 11 - Faculté des Sciences</orgName>
          <orgName type="acronym">UP11 UFR Sciences</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Campus universitaire d’Orsay - 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sciences.u-psud.fr/fr/index.html</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92966" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-12568" status="VALID">
          <idno type="IdRef">15551069X</idno>
          <idno type="RNSR">199914495P</idno>
          <idno type="ROR">https://ror.org/015d72457</idno>
          <orgName>Laboratoire de Mécanique des Structures et des Systèmes Couplés</orgName>
          <orgName type="acronym">LMSSC</orgName>
          <desc>
            <address>
              <addrLine>292, rue Saint Martin 75141 PARIS Cedex 03</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cnam.fr/lmssc/</ref>
          </desc>
          <listRelation>
            <relation name="EA3196" active="#struct-300351" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-92966" status="OLD">
          <idno type="ROR">https://ror.org/028rypz17</idno>
          <orgName>Université Paris-Sud - Paris 11</orgName>
          <orgName type="acronym">UP11</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-psud.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300351" status="VALID">
          <idno type="IdRef">027404978</idno>
          <idno type="ISNI">0000000121690459</idno>
          <idno type="ROR">https://ror.org/0175hh227</idno>
          <orgName>Conservatoire National des Arts et Métiers [Cnam]</orgName>
          <orgName type="acronym">Cnam</orgName>
          <desc>
            <address>
              <addrLine>292 Rue Saint-Martin, 75003 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cnam.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>