{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:GXVVR4I7YORL64TJIUJTNAK4R3","short_pith_number":"pith:GXVVR4I7","schema_version":"1.0","canonical_sha256":"35eb58f11fc3a2bf7269451336815c8ee88c3f8f049242a556c53d192129fa0d","source":{"kind":"arxiv","id":"2101.07267","version":2},"attestation_state":"computed","paper":{"title":"Training variational quantum algorithms is NP-hard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lennart Bittel, Martin Kliesch","submitted_at":"2021-01-18T19:00:01Z","abstract_excerpt":"Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground state problems from quantum chemistry and binary optimization problems, respectively. They are based on the idea of using a classical computer to train a parameterized quantum circuit. We show that the corresponding classical optimization problems are NP-hard. Moreover, the hardness is robust in the sense that, for every polynomial time algorithm, there are ins"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2101.07267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-01-18T19:00:01Z","cross_cats_sorted":[],"title_canon_sha256":"6ea4fb43f54d138ec00c9ccc715a3851577625925290df9f752fd8ab1a189b40","abstract_canon_sha256":"ebebdb87d26c4822670a24126f3ea0b188b10e83df9cfbd2c1b16e76c7ca45b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:14:36.584779Z","signature_b64":"praLpRdrurQswuXDRVTbW44JizUiA54b088S7/FLNL5EbLpejZ3zVLPd8LXdTdZ9ec5luq+d4fn9NS+cPVPjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35eb58f11fc3a2bf7269451336815c8ee88c3f8f049242a556c53d192129fa0d","last_reissued_at":"2026-07-05T04:14:36.584234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:14:36.584234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Training variational quantum algorithms is NP-hard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lennart Bittel, Martin Kliesch","submitted_at":"2021-01-18T19:00:01Z","abstract_excerpt":"Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground state problems from quantum chemistry and binary optimization problems, respectively. They are based on the idea of using a classical computer to train a parameterized quantum circuit. We show that the corresponding classical optimization problems are NP-hard. Moreover, the hardness is robust in the sense that, for every polynomial time algorithm, there are ins"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.07267","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.07267/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2101.07267","created_at":"2026-07-05T04:14:36.584305+00:00"},{"alias_kind":"arxiv_version","alias_value":"2101.07267v2","created_at":"2026-07-05T04:14:36.584305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.07267","created_at":"2026-07-05T04:14:36.584305+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXVVR4I7YORL","created_at":"2026-07-05T04:14:36.584305+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXVVR4I7YORL64TJ","created_at":"2026-07-05T04:14:36.584305+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXVVR4I7","created_at":"2026-07-05T04:14:36.584305+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08160","citing_title":"Weak Poincar\\'e Inequalities via Approximate Stochastic Localization: Application to Sampling the Sherrington-Kirkpatrick Model","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2403.02988","citing_title":"An Operational Framework for Nonclassicality in Quantum Communication Networks","ref_index":74,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3","json":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3.json","graph_json":"https://pith.science/api/pith-number/GXVVR4I7YORL64TJIUJTNAK4R3/graph.json","events_json":"https://pith.science/api/pith-number/GXVVR4I7YORL64TJIUJTNAK4R3/events.json","paper":"https://pith.science/paper/GXVVR4I7"},"agent_actions":{"view_html":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3","download_json":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3.json","view_paper":"https://pith.science/paper/GXVVR4I7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2101.07267&json=true","fetch_graph":"https://pith.science/api/pith-number/GXVVR4I7YORL64TJIUJTNAK4R3/graph.json","fetch_events":"https://pith.science/api/pith-number/GXVVR4I7YORL64TJIUJTNAK4R3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3/action/storage_attestation","attest_author":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3/action/author_attestation","sign_citation":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3/action/citation_signature","submit_replication":"https://pith.science/pith/GXVVR4I7YORL64TJIUJTNAK4R3/action/replication_record"}},"created_at":"2026-07-05T04:14:36.584305+00:00","updated_at":"2026-07-05T04:14:36.584305+00:00"}