{"id":"https://openalex.org/W3204280520","doi":"https://doi.org/10.26421/qic21.13-14-2","title":"On the extremal points of the \u039b-polytopes and classical simulation of quantum computation with magic states","display_name":"On the extremal points of the \u039b-polytopes and classical simulation of quantum computation with magic states","publication_year":2021,"publication_date":"2021-11-01","ids":{"openalex":"https://openalex.org/W3204280520","doi":"https://doi.org/10.26421/qic21.13-14-2","mag":"3204280520"},"language":"en","primary_location":{"id":"pmh:oai:repository.bilkent.edu.tr:11693/77467","is_oa":false,"landing_page_url":"http://hdl.handle.net/11693/77467","pdf_url":null,"source":{"id":"https://openalex.org/S4306400079","display_name":"Bilkent University Institutional Repository (Bilkent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I168864056","host_organization_name":"Bilkent University","host_organization_lineage":["https://openalex.org/I168864056"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum Information and Computation","raw_type":"Article"},"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011282980","display_name":"Cihan Okay","orcid":"https://orcid.org/0000-0001-8097-5227"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Okay, Cihan","raw_affiliation_strings":["Department of Mathematics, Bilkent University, Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080606237","display_name":"Michael Zurel","orcid":"https://orcid.org/0000-0003-0333-1174"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zurel, M.","raw_affiliation_strings":["Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada","Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020483167","display_name":"Robert Raussendorf","orcid":"https://orcid.org/0000-0003-4983-9213"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Raussendorf, R.","raw_affiliation_strings":["Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada","Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3993,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85181899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8455984592437744},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7574870586395264},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6606018543243408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5671656131744385},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5611443519592285},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.556609034538269},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5393552184104919},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.4634312093257904},{"id":"https://openalex.org/keywords/magic","display_name":"MAGIC (telescope)","score":0.42405933141708374},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41633981466293335},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4124714732170105},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.38614025712013245},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2718825936317444},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24239417910575867},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17915871739387512},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11734700202941895},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.10778051614761353}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8455984592437744},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7574870586395264},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6606018543243408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5671656131744385},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5611443519592285},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.556609034538269},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5393552184104919},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.4634312093257904},{"id":"https://openalex.org/C2777704519","wikidata":"https://www.wikidata.org/wiki/Q45732","display_name":"MAGIC (telescope)","level":2,"score":0.42405933141708374},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41633981466293335},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4124714732170105},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.38614025712013245},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2718825936317444},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24239417910575867},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17915871739387512},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11734700202941895},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.10778051614761353}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:repository.bilkent.edu.tr:11693/77467","is_oa":false,"landing_page_url":"http://hdl.handle.net/11693/77467","pdf_url":null,"source":{"id":"https://openalex.org/S4306400079","display_name":"Bilkent University Institutional Repository (Bilkent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I168864056","host_organization_name":"Bilkent University","host_organization_lineage":["https://openalex.org/I168864056"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum Information and Computation","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1490521149","https://openalex.org/W1731114062","https://openalex.org/W1966619759","https://openalex.org/W1994508806","https://openalex.org/W2005144372","https://openalex.org/W2036481581","https://openalex.org/W2036604884","https://openalex.org/W2053987271","https://openalex.org/W2055199227","https://openalex.org/W2109741106","https://openalex.org/W2145928944","https://openalex.org/W2299781645","https://openalex.org/W2524307097","https://openalex.org/W2764347725","https://openalex.org/W2945490636","https://openalex.org/W2957955710","https://openalex.org/W3015004104","https://openalex.org/W3101548872","https://openalex.org/W3101778975","https://openalex.org/W3102057473","https://openalex.org/W3105454500","https://openalex.org/W3106326670","https://openalex.org/W4242275969"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4289703404","https://openalex.org/W4387265813","https://openalex.org/W4320410061","https://openalex.org/W2951363717","https://openalex.org/W2134613344"],"abstract_inverted_index":{"We":[0,35],"investigate":[1],"the":[2,12,40,68,82,87,104,108,123,134],"\u039b-polytopes,":[3],"a":[4,94],"convex-linear":[5],"structure":[6],"recently":[7],"defined":[8],"and":[9],"applied":[10],"to":[11,53,81],"classical":[13,69,83,111,128],"simulation":[14,70,84,112,129],"of":[15,33,39,71,97,110,121,130],"quantum":[16,72,131],"computation":[17,73],"with":[18,74],"magic":[19,75],"states":[20,76],"by":[21],"sampling.":[22],"There":[23],"is":[24,102],"one":[25],"such":[26],"polytope,":[27],"\u039bn,":[28,57,122],"for":[29,58,117],"every":[30],"number":[31],"n":[32],"qubits.":[34],"establish":[36],"two":[37],"properties":[38],"family":[41],"{\u039bn,n\u2208N},":[42],"namely":[43],"(i)":[44],"Any":[45],"extremal":[46,119],"point":[47],"(vertex)":[48],"A\u03b1\u2208\u039bm":[49],"can":[50,77],"be":[51,78],"used":[52],"construct":[54],"vertices":[55,63,98],"in":[56,99],"all":[59],"n>m.":[60],"(ii)":[61],"For":[62],"obtained":[64],"through":[65],"this":[66],"mapping,":[67],"efficiently":[79],"reduced":[80],"based":[85],"on":[86],"preimage":[88],"A\u03b1.":[89],"In":[90],"addition,":[91],"we":[92],"describe":[93],"new":[95],"class":[96],"\u039b2":[100],"which":[101],"outside":[103],"known":[105,136],"classification.":[106],"While":[107],"hardness":[109],"remains":[113],"an":[114],"open":[115],"problem":[116],"most":[118],"points":[120],"above":[124],"results":[125],"extend":[126],"efficient":[127],"computations":[132],"beyond":[133],"presently":[135],"range.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}