{"paper":{"title":"Geometric Preconditioning and Curriculum Optimization for Trainable Variational Quantum Regression","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"A capacity-controlled classical embedding acts as a learnable geometric preconditioner to improve trainability of variational quantum circuits for regression.","cross_cats":["quant-ph"],"primary_cat":"cs.LG","authors_text":"Qingyu Meng, Yangshuai Wang","submitted_at":"2026-01-17T07:32:18Z","abstract_excerpt":"Variational quantum circuits are increasingly studied as continuous-function approximators, but quantum regression remains difficult to train when global losses, finite-shot stochasticity, and circuit-depth growth combine to produce weak or ill-conditioned gradient signals. We study this trainability problem in a controlled hybrid quantum--classical regression design. The central ingredient is a capacity-controlled classical embedding that acts as a learnable geometric preconditioner: it reshapes the input distribution seen by a data-reuploading variational circuit while preserving a low-dimen"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Across finite-size statevector audits on PDE-informed regression benchmarks and small-data tabular tasks, the Hybrid QNN lowers error relative to Pure QNN baselines under matched quantum-model budgets.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The classical embedding successfully acts as a learnable geometric preconditioner that reshapes the empirical Gram matrix to improve residual contraction in the linearized quantum-parameter dynamics, without the capacity control introducing new ill-conditioning that offsets the benefit.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A hybrid variational quantum regression design with classical geometric preconditioning and curriculum optimization improves trainability over pure quantum models while remaining behind strong classical baselines.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A capacity-controlled classical embedding acts as a learnable geometric preconditioner to improve trainability of variational quantum circuits for regression.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"dc8f25d92ea678c7743c19d0d63b5cfc23dcb1eb753f49038e7a322cba68869c"},"source":{"id":"2601.11942","kind":"arxiv","version":3},"verdict":{"id":"24e981f6-c95e-408d-af21-3369e6478de7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T13:10:28.472850Z","strongest_claim":"Across finite-size statevector audits on PDE-informed regression benchmarks and small-data tabular tasks, the Hybrid QNN lowers error relative to Pure QNN baselines under matched quantum-model budgets.","one_line_summary":"A hybrid variational quantum regression design with classical geometric preconditioning and curriculum optimization improves trainability over pure quantum models while remaining behind strong classical baselines.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The classical embedding successfully acts as a learnable geometric preconditioner that reshapes the empirical Gram matrix to improve residual contraction in the linearized quantum-parameter dynamics, without the capacity control introducing new ill-conditioning that offsets the benefit.","pith_extraction_headline":"A capacity-controlled classical embedding acts as a learnable geometric preconditioner to improve trainability of variational quantum circuits for regression."},"references":{"count":36,"sample":[{"doi":"","year":2021,"title":"The power of quantum neural networks.Nature Computa- tional Science, 1(6):403–409,","work_id":"9ebc46e0-a671-4c96-bfa6-1c3f18b36d6d","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"UCI machine learning repository,","work_id":"d26af7bf-88e1-4286-ba07-aa5d55c1c272","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Training deep quan- tum neural networks.Nature communications, 11(1):808,","work_id":"b321b655-fb0b-40c1-8839-671237b4aa5a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Trainable embedding quantum physics informed neural networks for solving nonlinear pdes.Sci- entific Reports, 15(1):18823,","work_id":"6d0ae0d6-bd54-48bb-b715-bb1fd7d2dd12","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"J., Farkas, M., Killoran, N","work_id":"c361f579-4f45-4544-a6b5-27565fec14a4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":36,"snapshot_sha256":"0e027e0a678bfa0e7541a350895a11e3ac6a1717afa9b922a5edbc783d77492e","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"30210bb21e03697ad68e283e87307bace8f269cf7214f7e9c942b371ab7e922c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}