{"paper":{"title":"Quantum-Accelerated Gowers $U_2$ Norm for Bent Boolean Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Quantum circuit evaluates Gowers U2 norm using 3n qubits and O(n^2) gates for bent function search","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C. A. Jothiwashran, Rajdeep Dwivedi, Sugata Gangopadhyay, Vishvendra Singh Poonia","submitted_at":"2026-04-28T11:05:20Z","abstract_excerpt":"Bent Boolean functions extremal objects that maximally resist affine approximation are notoriously hard to construct for large numbers of variables. We propose a hybrid quantum-classical genetic algorithm (GA) that uses a quantum circuit to evaluate the Gowers $U_2$ norm as the evolutionary fitness function. Our central contribution is a complexity-theoretic separation: the quantum evaluation circuit requires only $3n$ qubits and $\\bigO(n^2)$ two-qubit gates per function query, whereas the classical computation of the exact Gowers $U_2$ norm demands $\\bigO(2^{2n})$ arithmetic operations an exp"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the quantum evaluation circuit requires only 3n qubits and O(n^2) two-qubit gates per function query, whereas the classical computation of the exact Gowers U2 norm demands O(2^{2n}) arithmetic operations an exponential overhead that renders it infeasible for n ≳ 25","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The quantum circuit correctly evaluates the Gowers U2 norm up to sampling noise that does not derail the genetic algorithm's ability to reach the bent threshold, and that fault-tolerant hardware will be available to run the circuit at the claimed gate counts.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A quantum circuit computes the Gowers U2 norm using 3n qubits and O(n^2) gates to accelerate genetic search for bent Boolean functions, providing exponential advantage over classical O(2^{2n}) evaluation for n greater than 25.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Quantum circuit evaluates Gowers U2 norm using 3n qubits and O(n^2) gates for bent function search","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"def9ea45b0c068416dae9bc6fa414adc625076b63bb0ec33cb69dd6347a527c5"},"source":{"id":"2604.25503","kind":"arxiv","version":3},"verdict":{"id":"d8eff787-086f-4eea-a29b-0555716f3893","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T16:36:16.613412Z","strongest_claim":"the quantum evaluation circuit requires only 3n qubits and O(n^2) two-qubit gates per function query, whereas the classical computation of the exact Gowers U2 norm demands O(2^{2n}) arithmetic operations an exponential overhead that renders it infeasible for n ≳ 25","one_line_summary":"A quantum circuit computes the Gowers U2 norm using 3n qubits and O(n^2) gates to accelerate genetic search for bent Boolean functions, providing exponential advantage over classical O(2^{2n}) evaluation for n greater than 25.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The quantum circuit correctly evaluates the Gowers U2 norm up to sampling noise that does not derail the genetic algorithm's ability to reach the bent threshold, and that fault-tolerant hardware will be available to run the circuit at the claimed gate counts.","pith_extraction_headline":"Quantum circuit evaluates Gowers U2 norm using 3n qubits and O(n^2) gates for bent function search"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.25503/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T04:39:26.599052Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:06:04.269779Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d5564a49047929ab834dd326a5070d48ed68e554d773c89534cbf0cc2fa9c504"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}