{"id":"https://openalex.org/W7220712975","doi":"https://doi.org/10.48550/arxiv.2610.03800","title":"Exponentially Compressed and Garbage-Free Alias Sampling for Polynomial State Preparation","display_name":"Exponentially Compressed and Garbage-Free Alias Sampling for Polynomial State Preparation","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220712975","doi":"https://doi.org/10.48550/arxiv.2610.03800"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03800","pdf_url":"https://arxiv.org/pdf/2610.03800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.03800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157784465","display_name":"Diyi Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liu, Diyi","raw_affiliation_strings":["Lawrence Berkeley National Laboratory , Berkeley , California 94720 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory , Berkeley , California 94720 , USA","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100713368","display_name":"Hanyu Wang","orcid":"https://orcid.org/0009-0007-5230-9615","observed_orcids":["https://orcid.org/0009-0007-5230-9615"]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Hanyu","raw_affiliation_strings":["Department of Computer Science , University of California , Los Angeles , California 90095 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , University of California , Los Angeles , California 90095 , USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157768366","display_name":"Shuchen Zhu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Shuchen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016776689","display_name":"Jason Cong","orcid":"https://orcid.org/0000-0003-2887-6963","observed_orcids":["https://orcid.org/0000-0003-2887-6963"]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cong, Jason","raw_affiliation_strings":["Department of Computer Science , University of California , Los Angeles , California 90095 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , University of California , Los Angeles , California 90095 , USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034688782","display_name":"Wibe Albert de Jong","orcid":"https://orcid.org/0000-0002-7114-8315","observed_orcids":["https://orcid.org/0000-0002-7114-8315"]},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"de Jong, Wibe Albert","raw_affiliation_strings":["Lawrence Berkeley National Laboratory , Berkeley , California 94720 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory , Berkeley , California 94720 , USA","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007317870","display_name":"David B. Williams\u2010Young","orcid":"https://orcid.org/0000-0003-2735-3706","observed_orcids":["https://orcid.org/0000-0003-2735-3706"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Williams-Young, David","raw_affiliation_strings":["Microsoft Quantum , Redmond , Washington 98052 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Quantum , Redmond , Washington 98052 , USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157732832","display_name":"Chao Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yang, Chao","raw_affiliation_strings":["Lawrence Berkeley National Laboratory , Berkeley , California 94720 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory , Berkeley , California 94720 , USA","institution_ids":["https://openalex.org/I148283060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":1.0,"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":1.0,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.0,"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/T11804","display_name":"Quantum many-body systems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/block-encoding","display_name":"block encoding","score":0.8889999985694885},{"id":"https://openalex.org/keywords/qubitization","display_name":"qubitization","score":0.9599999785423279},{"id":"https://openalex.org/keywords/quantum-singular-value-transformation","display_name":"quantum singular value transformation","score":0.9330000281333923},{"id":"https://openalex.org/keywords/clifford-t-circuits","display_name":"Clifford+T circuits","score":0.8149999976158142},{"id":"https://openalex.org/keywords/quantum-state-preparation","display_name":"quantum state preparation","score":0.4749999940395355},{"id":"https://openalex.org/keywords/quantum-simulation","display_name":"quantum simulation","score":0.527999997138977}],"concepts":[{"id":"https://openalex.org/C46681722","wikidata":"https://www.wikidata.org/wiki/Q4725589","display_name":"Alias","level":2,"score":0.6953999996185303},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5688999891281128},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5281999707221985},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5264999866485596},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.5145999789237976},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.47110000252723694},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4699000120162964},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4652999937534332},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.39419999718666077},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.36160001158714294},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.36059999465942383},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.35429999232292175},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.35339999198913574},{"id":"https://openalex.org/C134835016","wikidata":"https://www.wikidata.org/wiki/Q690265","display_name":"Lookup table","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3400999903678894},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.32899999618530273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29420000314712524},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2847999930381775},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2782999873161316},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.25949999690055847}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03800","pdf_url":"https://arxiv.org/pdf/2610.03800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.03800","doi":"https://doi.org/10.48550/arxiv.2610.03800","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03800","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03800","pdf_url":"https://arxiv.org/pdf/2610.03800","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5483170187","display_name":"NQVL:QSTD:Design: Open-Stack Rydberg Atom Quantum Computing Laboratory (ORAQL)","funder_award_id":"2533041","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220712975.pdf","grobid_xml":"https://content.openalex.org/works/W7220712975.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4307479171","https://openalex.org/W2072498431","https://openalex.org/W4398191985","https://openalex.org/W7138850353","https://openalex.org/W4393032694","https://openalex.org/W4390575965","https://openalex.org/W7161756081","https://openalex.org/W4403621970","https://openalex.org/W1657809206","https://openalex.org/W7106006073"],"abstract_inverted_index":{"Coherent":[0],"alias":[1,48,106,173,197],"sampling":[2,181,206],"implement":[3,28],"an":[4],"important":[5],"subroutine":[6],"for":[7,31,102,108,124,146,179,189],"block":[8,29],"encoding":[9],"and":[10,24,45,53,80,94,153,160],"qubitization":[11],"based":[12,207],"quantum":[13,16,34,54,95,100],"simulation":[14],"using":[15,111],"lookup":[17,23],"table.":[18],"Related":[19],"constructions":[20],"exploit":[21],"data":[22],"matrix":[25],"structure":[26],"to":[27],"encodings":[30],"use":[32],"in":[33,57,86,205],"singular":[35],"value":[36],"transformation.":[37],"For":[38],"a":[39,68,99,121,131,186,202],"state":[40,147,209],"on":[41],"$n$":[42,152],"qubits,":[43],"constructing":[44],"storing":[46],"the":[47,63,75,105,142,161,168,172,191],"table":[49,76,107,174],"requires":[50],"both":[51],"classical":[52,93,180],"resources":[55],"exponential":[56],"$n$.":[58],"We":[59,97],"show":[60],"that":[61],"when":[62],"amplitudes":[64],"are":[65],"samples":[66],"of":[67,70,135,171],"polynomial":[69,85,109,126],"degree":[71],"at":[72],"most":[73],"$d$,":[74,88,154],"can":[77,175],"be":[78,177],"represented":[79],"evaluated":[81],"coherently":[82,103],"with":[83,130,150],"cost":[84],"$n$,":[87],"exponentially":[89],"reduced":[90],"from":[91],"$\u0398(2^n)$":[92],"cost.":[96],"construct":[98,120],"circuit":[101,123],"computing":[104],"states":[110,127],"reversible":[112],"integer":[113],"arithmetic.":[114],"By":[115],"employing":[116],"fast":[117],"arithmetic,":[118],"we":[119,184],"deterministic":[122],"preparing":[125],"over":[128],"Clifford+$T$":[129],"complete":[132,162],"gate":[133,163],"count":[134,164],"$\\tilde{O}(ndB+B^2)$,":[136],"where":[137],"arithmetic":[138],"width":[139],"$B=\\tilde{O}(dn+d\\log(d+1))$.":[140],"In":[141],"high":[143],"precision":[144],"limit":[145],"fidelity":[148],"$\u03b5$":[149],"fixed":[151],"it":[155],"is":[156],"sufficient":[157],"have":[158],"$B=\u0398(\\log(1/\u03b5))$":[159],"becomes":[165],"$O(\\log^3(1/\u03b5)\\log\\log(1/\u03b5))$.":[166],"Additionally,":[167],"effective":[169],"representation":[170],"also":[176],"used":[178],"algorithms.":[182],"Furthermore,":[183],"develop":[185],"novel":[187],"technique":[188,200],"uncomputing":[190],"auxilary":[192],"register":[193],"generated":[194],"by":[195],"coherent":[196],"sampling.":[198],"This":[199],"opens":[201],"research":[203],"direction":[204],"initial":[208],"preparation.":[210]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-07T00:00:00"}
