{"paper":{"title":"MLMC-qDRIFT: Multilevel Variance Reduction for Randomized Quantum Hamiltonian Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε)).","cross_cats":["cs.NA","math.NA"],"primary_cat":"quant-ph","authors_text":"Pegah Mohammadipour, Xiantao Li","submitted_at":"2026-04-29T16:32:48Z","abstract_excerpt":"Simulating quantum dynamics is one of the central applications of quantum computing. For Hamiltonians written as a sum of many terms, deterministic Trotter--Suzuki product formulas can require applying a large number of term-wise evolutions at each time step, leading to high circuit costs for large or dense systems. Randomized methods such as qDRIFT offer an alternative: each step samples only one Hamiltonian term, giving a circuit depth with no explicit dependence on the number of terms. However, when qDRIFT is used for observable estimation, high precision requires many independent random ci"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the resulting MLMC-qDRIFT estimator reduces the total gate complexity for fixed-precision observable estimation from the standard qDRIFT scaling O(ε^{-3}) to O(ε^{-2} log²(1/ε)), while preserving qDRIFT's lack of explicit dependence on the number of Hamiltonian terms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The variance of the coupled level differences decays sufficiently fast with increasing circuit depth so that the multilevel estimator achieves the claimed complexity improvement.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"MLMC-qDRIFT achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε)).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"91731d9f8f00462d191554b363bcc6c44f74620a39ea57d7ca4733f5367d43c8"},"source":{"id":"2604.26865","kind":"arxiv","version":2},"verdict":{"id":"2cc4ac67-1dad-46e1-b01c-c8fdb0e80920","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T13:08:12.908237Z","strongest_claim":"We prove that the resulting MLMC-qDRIFT estimator reduces the total gate complexity for fixed-precision observable estimation from the standard qDRIFT scaling O(ε^{-3}) to O(ε^{-2} log²(1/ε)), while preserving qDRIFT's lack of explicit dependence on the number of Hamiltonian terms.","one_line_summary":"MLMC-qDRIFT achieves O(ε^{-2} log²(1/ε)) gate complexity for observable estimation in quantum dynamics by using coupled multilevel qDRIFT estimators with variance decay across levels.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The variance of the coupled level differences decays sufficiently fast with increasing circuit depth so that the multilevel estimator achieves the claimed complexity improvement.","pith_extraction_headline":"A multilevel coupling of qDRIFT estimators reduces total gate complexity for observable estimation from O(ε^{-3}) to O(ε^{-2} log²(1/ε))."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26865/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T19:44:32.237201Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4a9f2f8274ea782e7f57d549bd6deb576d75fb15b9193e488fb7f4da3ef60237"},"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"}