{"paper":{"title":"Entanglement Distance of Two- and Multi-Qubit Variational States and Its Quantification with Quantum Computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Recurrence relations on Pauli observables yield exact entanglement distances for RY-CZ variational circuits on qubit chains.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kh. P. Gnatenko, M. Z. Seniak, R. O. Hredil, V. Y. Pinchuk, Y. T. Shevchuk","submitted_at":"2026-04-30T21:53:39Z","abstract_excerpt":"We study the entanglement distance of variational quantum states for two-qubit and multi-qubit systems. These states are constructed using variational quantum circuits with $R_Y$ rotations and entangling $CZ$ gates. For the two-qubit case, we analytically derive recurrence relations for expectation values of Pauli observables. This approach allows us to calculate quantum correlators and evaluate the entanglement distance as a function of the circuit parameters and depth. The analysis was extended to a closed one-dimensional chain of $N$ qubits. An explicit analytical expression for the entangl"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"With increasing circuit depth, more qubits influence a given qubit, which reflects the spreading of quantum correlations in the system. For a closed one-dimensional chain of N qubits, explicit analytical expressions are derived for the case of two layers.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The recurrence relations derived from the specific layered structure of RY and CZ gates fully capture the expectation values of all relevant Pauli observables without additional approximations or truncation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Recurrence relations yield analytical expressions for entanglement distance in variational qubit states, revealing how correlations spread with circuit depth in one-dimensional chains.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Recurrence relations on Pauli observables yield exact entanglement distances for RY-CZ variational circuits on qubit chains.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1f573fd3ee61115b7fb5d91c2bfab6b7507586ec9f71decd674ab415fc7f317e"},"source":{"id":"2605.00259","kind":"arxiv","version":2},"verdict":{"id":"23b6b0cd-a5ee-4e9a-9086-ddbbf0ade8d0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T19:46:21.959676Z","strongest_claim":"With increasing circuit depth, more qubits influence a given qubit, which reflects the spreading of quantum correlations in the system. For a closed one-dimensional chain of N qubits, explicit analytical expressions are derived for the case of two layers.","one_line_summary":"Recurrence relations yield analytical expressions for entanglement distance in variational qubit states, revealing how correlations spread with circuit depth in one-dimensional chains.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The recurrence relations derived from the specific layered structure of RY and CZ gates fully capture the expectation values of all relevant Pauli observables without additional approximations or truncation.","pith_extraction_headline":"Recurrence relations on Pauli observables yield exact entanglement distances for RY-CZ variational circuits on qubit chains."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00259/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T20:35:39.743662Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:22:35.026095Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"2e1a632980c3b97f5e5fa9ee921a3f4b136f84447e6d80c1f8df595ce776beba"},"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"}