{"paper":{"title":"QAC0 Can Prepare Every Logarithmic-Qubit State","arxiv_id":"2609.17408","primary_cat":"quant-ph","submitted_at":"2026-09-15T16:35:52+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"$\\mathsf{QAC}^0$ is the class of constant-depth $\\mathrm{poly}(n)$-ancilla circuits obtained by extending $\\mathsf{QNC}^0$, the class of local circuits, to include nonlocal interactions via arbitrary width Toffoli gates.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.44,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":1.0,"id":"s1","own":false,"role":"background","text":"It is believed to be weaker than its counterpart, $\\mathsf{QNC}^0_f$, obtained by including arbitrary-width FANOUT gates instead ($\\mathsf{QAC}^0 \\subseteq \\mathsf{QNC}^0_f$ [Moo99]).","hedge":{"p":0.77,"label":"hedged_possibility"},"own_p":0.04,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.88,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.68,"id":"s2","own":true,"role":"result","text":"In this note, we show that every $O(\\log n)$-qubit state can be exactly and cleanly prepared by a $\\mathrm{poly}(n)$-ancilla $\\mathsf{QAC}^0$ circuit.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.97,"quantitative":true,"quantitative_p":0.93,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.68,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.32,"interpretation":0.0}},{"i":3,"p":0.93,"id":"s3","own":false,"role":"gap","text":"Previous known $\\mathrm{poly}(n)$-ancilla circuits for arbitrary such states are only known via additional access to either FANOUT or QRAM (indexing) gates [Ros21b, GGJ26b], neither of which are known to be in $\\mathsf{QAC}^0$.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.04,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.45,"role_probabilities":{"gap":0.93,"method":0.0,"result":0.0,"background":0.07,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.67,"id":"s4","own":true,"role":"interpretation","text":"Equivalently, prior constructions of arbitrary $n$-qubit states in $\\mathsf{QAC}^0$ require doubly exponential size and we obtain an exponential factor improvement.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.83,"main_claim_p":0.13,"quantitative":true,"quantitative_p":0.98,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.29,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.67}}]},"compiled":{"main_claim":{"p":1.0,"text":"In this note, we show that every $O(\\log n)$-qubit state can be exactly and cleanly prepared by a $\\mathrm{poly}(n)$-ancilla $\\mathsf{QAC}^0$ circuit.","location":"abstract s2","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":4629,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.6,"states_limitation":0.2,"human_participants":0.01,"controlled_comparison":0.17,"randomized_assignment":0.01,"states_quantitative_result":0.92,"compares_with_prior_results":0.98,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.99,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.01,"proof_or_derivation":0.99,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.99,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.01,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.99,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":1.0,"text":"In this note, we show that every $O(\\log n)$-qubit state can be exactly and cleanly prepared by a $\\mathrm{poly}(n)$-ancilla $\\mathsf{QAC}^0$ circuit.","location":"abstract s2"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":5,"sentences_in_abstract":5},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}