{"paper":{"title":"Fraxonium: Fractional fluxon states for qudit encoding","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A superconducting circuit generalizes the fluxonium using fractional fluxon states for protected qudit encoding.","cross_cats":["cond-mat.mes-hall"],"primary_cat":"quant-ph","authors_text":"Gianluigi Catelani, Luca Chirolli, Luigi Amico, Uri Vool, Valentina Brosco","submitted_at":"2026-05-14T08:58:07Z","abstract_excerpt":"We propose a superconducting circuit hosting $d$ low-lying states, well separated from the rest of the spectrum, that naturally realizes a qudit system protected from leakage errors. The system represents a generalization of the fluxonium and the low-energy states are constituted by fractional fluxon states, that we call {\\it fraxons}, localized in the minima of a suitably designed Josephson potential. The latter is tailored through a Fourier engineering approach, that employs multi-harmonic Josephson building block elements composed by a Josephson junction and an inductance connected in serie"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The system represents a generalization of the fluxonium and the low-energy states are constituted by fractional fluxon states, that we call fraxons, localized in the minima of a suitably designed Josephson potential.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"A suitably designed Josephson potential can be realized through Fourier engineering with multi-harmonic elements such that d low-lying fractional fluxon states remain well separated from the rest of the spectrum.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Superconducting circuit hosts fractional fluxon states (fraxons) in a tailored Josephson potential to realize protected qudits with a STIRAP gate protocol.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A superconducting circuit generalizes the fluxonium using fractional fluxon states for protected qudit encoding.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"936dfee4c0b3b4d4d83afbb20acdf8f2363ee81032f490972e9627aeea41f65e"},"source":{"id":"2605.14586","kind":"arxiv","version":1},"verdict":{"id":"5a704302-43b2-4c69-b60e-0db74a8fc489","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:24:42.507682Z","strongest_claim":"The system represents a generalization of the fluxonium and the low-energy states are constituted by fractional fluxon states, that we call fraxons, localized in the minima of a suitably designed Josephson potential.","one_line_summary":"Superconducting circuit hosts fractional fluxon states (fraxons) in a tailored Josephson potential to realize protected qudits with a STIRAP gate protocol.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"A suitably designed Josephson potential can be realized through Fourier engineering with multi-harmonic elements such that d low-lying fractional fluxon states remain well separated from the rest of the spectrum.","pith_extraction_headline":"A superconducting circuit generalizes the fluxonium using fractional fluxon states for protected qudit encoding."},"references":{"count":146,"sample":[{"doi":"","year":null,"title":"All the branches are connected in parallel, with a fluxπ/2 between the four equal modular elements","work_id":"4d975859-aa59-4315-b96b-362289808875","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Ω3Ω#=Ω Ω3 |2⟩|1⟩|0⟩ |𝑢⟩ Ω!Ω#Ω","work_id":"c2719d32-1108-47ec-ba98-07c8ad6e59fd","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Tight-binding model Following [107], we can model the dynamics between the fluxon states localized in the minima of the effective transmon potential through a tight-binding approach. The fluxon states","work_id":"a72c6e95-d1ed-4c75-ac0e-f2a339a09dbe","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"cos[φx −π(m−n)/2] −E J Dmn( √ 2σ) cos[2φx −π(m−n)/2],(D4) In the working regimeE J ≫E C, EL, the level spacing provided by √8ECEL is small compared toE J and a large number of Fock states is needed to","work_id":"ac87b359-1a18-42e8-a6f3-85e60a4b6949","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"P. W. Shor, Scheme for reducing decoherence in quan- tum computer memory, Phys. Rev. A52, R2493 (1995)","work_id":"ade9b5a3-b3e9-4d29-886a-cee4bc3325f5","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":146,"snapshot_sha256":"9fb5bcce2519513482c7f6995ac7d004b1d2348a1c221b8ea955b80c12f65a52","internal_anchors":2},"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"}