{"id":"https://openalex.org/W4411067281","doi":"https://doi.org/10.22331/q-2025-06-05-1766","title":"Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation","display_name":"Stabilizer codes for Heisenberg-limited many-body Hamiltonian estimation","publication_year":2025,"publication_date":"2025-06-05","ids":{"openalex":"https://openalex.org/W4411067281","doi":"https://doi.org/10.22331/q-2025-06-05-1766"},"language":"en","primary_location":{"id":"doi:10.22331/q-2025-06-05-1766","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-06-05-1766","pdf_url":"https://quantum-journal.org/papers/q-2025-06-05-1766/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2025-06-05-1766/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115458112","display_name":"Santanu Bosu Antu","orcid":null},"institutions":[{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Santanu Bosu Antu","raw_affiliation_strings":["Department of Applied Physics and Yale Quantum Institute, New Haven, Connecticut 06520, USA","Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Physics and Yale Quantum Institute, New Haven, Connecticut 06520, USA","institution_ids":[]},{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada","institution_ids":["https://openalex.org/I183974707"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033264921","display_name":"Sisi Zhou","orcid":"https://orcid.org/0000-0003-4618-8590"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sisi Zhou","raw_affiliation_strings":["Department of Physics and Astronomy, Department of Applied Mathematics, and Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1, Canada","Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, Department of Applied Mathematics, and Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada","institution_ids":["https://openalex.org/I183974707"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5115458112"],"corresponding_institution_ids":["https://openalex.org/I183974707"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06195476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":null,"first_page":"1766","last_page":"1766"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9972000122070312,"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":0.9972000122070312,"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":0.9919000267982483,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9301999807357788,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stabilizer","display_name":"Stabilizer (aeronautics)","score":0.7156277894973755},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5921643376350403},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38105738162994385},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3440595865249634},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2707980275154114},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.15066131949424744},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.08200180530548096}],"concepts":[{"id":"https://openalex.org/C2777502316","wikidata":"https://www.wikidata.org/wiki/Q2712515","display_name":"Stabilizer (aeronautics)","level":2,"score":0.7156277894973755},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5921643376350403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38105738162994385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3440595865249634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2707980275154114},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.15066131949424744},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.08200180530548096}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2025-06-05-1766","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-06-05-1766","pdf_url":"https://quantum-journal.org/papers/q-2025-06-05-1766/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:be35f278948541db98b44938cebe783f","is_oa":true,"landing_page_url":"https://doaj.org/article/be35f278948541db98b44938cebe783f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 9, p 1766 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2025-06-05-1766","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-06-05-1766","pdf_url":"https://quantum-journal.org/papers/q-2025-06-05-1766/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411067281.pdf","grobid_xml":"https://content.openalex.org/works/W4411067281.grobid-xml"},"referenced_works_count":83,"referenced_works":["https://openalex.org/W1578322733","https://openalex.org/W1964601808","https://openalex.org/W1981935016","https://openalex.org/W1981983416","https://openalex.org/W1983447989","https://openalex.org/W1985596398","https://openalex.org/W1993122650","https://openalex.org/W1993488859","https://openalex.org/W1999664967","https://openalex.org/W1999706070","https://openalex.org/W2007948277","https://openalex.org/W2015683881","https://openalex.org/W2015876000","https://openalex.org/W2030867075","https://openalex.org/W2032839191","https://openalex.org/W2042474962","https://openalex.org/W2051618454","https://openalex.org/W2051869207","https://openalex.org/W2060532199","https://openalex.org/W2060887031","https://openalex.org/W2061512838","https://openalex.org/W2064517571","https://openalex.org/W2076021266","https://openalex.org/W2078635972","https://openalex.org/W2083423624","https://openalex.org/W2088636071","https://openalex.org/W2114207424","https://openalex.org/W2124596515","https://openalex.org/W2130062294","https://openalex.org/W2135273380","https://openalex.org/W2145801399","https://openalex.org/W2160139326","https://openalex.org/W2169656062","https://openalex.org/W2319651424","https://openalex.org/W2487737115","https://openalex.org/W2591067744","https://openalex.org/W2595654587","https://openalex.org/W2608205557","https://openalex.org/W2622552587","https://openalex.org/W2763302490","https://openalex.org/W2767966692","https://openalex.org/W2772017661","https://openalex.org/W2775064897","https://openalex.org/W2805784967","https://openalex.org/W2850096078","https://openalex.org/W2876655733","https://openalex.org/W2898842402","https://openalex.org/W2900404755","https://openalex.org/W2950894932","https://openalex.org/W2980596263","https://openalex.org/W2990961515","https://openalex.org/W2996245700","https://openalex.org/W3010503692","https://openalex.org/W3037089521","https://openalex.org/W3037447387","https://openalex.org/W3081551465","https://openalex.org/W3098250312","https://openalex.org/W3099680657","https://openalex.org/W3100736866","https://openalex.org/W3100777706","https://openalex.org/W3101516197","https://openalex.org/W3102240611","https://openalex.org/W3104157705","https://openalex.org/W3104643420","https://openalex.org/W3105439835","https://openalex.org/W3127800349","https://openalex.org/W3128860145","https://openalex.org/W3138690126","https://openalex.org/W3143400115","https://openalex.org/W3181660950","https://openalex.org/W3207755657","https://openalex.org/W4281394052","https://openalex.org/W4287993384","https://openalex.org/W4313227165","https://openalex.org/W4321610982","https://openalex.org/W4376639827","https://openalex.org/W4382726830","https://openalex.org/W4389097682","https://openalex.org/W4389373471","https://openalex.org/W4394621975","https://openalex.org/W4404106814","https://openalex.org/W4404713023","https://openalex.org/W6958769664"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Estimating":[0],"many-body":[1,97],"Hamiltonians":[2,98],"has":[3],"wide":[4],"applications":[5],"in":[6,76,95,218],"quantum":[7,14,65,73,91,123],"technology.":[8],"By":[9],"allowing":[10],"coherent":[11],"evolution":[12],"of":[13,23,46,89,116,134,153],"systems":[15],"and":[16,48,67,126,145,168,174,207],"entanglement":[17],"across":[18],"multiple":[19],"probes,":[20],"the":[21,44,52,56,87,132,163,169,192,198,210],"precision":[22],"estimating":[24,96,102],"a":[25,103,213],"fully":[26,104],"connected":[27,105],"<mml:math":[28,35,41,49,106,135,140,146,158,172,193,200],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>-body":[29],"interaction":[30,108],"can":[31,188],"scale":[32],"up":[33],"to":[34,71,78],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo":[36,136,141,147],"stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mi>k</mml:mi></mml:msup><mml:mi>t</mml:mi><mml:msup><mml:mo":[37],"stretchy=\"false\">)</mml:mo><mml:mrow":[38,138,143,149],"class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>,":[39,139,150],"where":[40],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>":[42],"is":[43,51,69,204],"number":[45],"probes":[47],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>":[50],"probing":[53],"time.":[54],"However,":[55],"optimal":[57,156,199],"scaling":[58,170,203],"may":[59],"no":[60],"longer":[61],"be":[62],"achievable":[63,205],"under":[64,99,109],"noise,":[66,111],"it":[68],"important":[70],"apply":[72],"error":[74,92],"correction":[75],"order":[77],"recover":[79],"this":[80,83],"limit.":[81],"In":[82],"work,":[84],"we":[85,112,181],"study":[86],"performance":[88],"stabilizer":[90,117,166,186],"correcting":[93],"codes":[94,118,125,128,183],"noise.":[100],"When":[101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Z</mml:mi><mml:mi>Z</mml:mi><mml:mi>Z</mml:mi></mml:math>":[107],"single-qubit":[110],"showcase":[113],"three":[114],"families":[115],"\u2013":[119,129],"thin":[120],"surface":[121],"codes,":[122],"Reed\u2013Muller":[124],"Shor":[127,219],"that":[130],"achieve":[131,191],"scalings":[133],"stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:msup><mml:mo":[137],"stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mi>t</mml:mi><mml:msup><mml:mo":[142],"class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>":[144,195],"stretchy=\"false\">(</mml:mo><mml:msup><mml:mi>n</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mi>t</mml:mi><mml:msup><mml:mo":[148],"respectively,":[151],"all":[152],"which":[154],"are":[155],"with":[157,171,184],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>.":[159],"We":[160],"further":[161],"discuss":[162],"relation":[164],"between":[165],"structure":[167],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>,":[173],"identify":[175],"several":[176],"no-go":[177],"theorems.":[178],"For":[179],"instance,":[180],"find":[182],"constant-weight":[185],"generators":[187],"at":[189],"most":[190],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>n</mml:mi><mml:mrow":[194,201],"scaling,":[196],"while":[197],"class=\"MJX-TeXAtom-ORD\"><mml:mo>&amp;#x2212;</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>":[202],"if":[206,209],"only":[208],"code":[211,215],"bears":[212],"repetition":[214],"substructure,":[216],"like":[217],"code.":[220]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
