{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:B2TZ7OFGRWXTZL346LPIQQCA7L","short_pith_number":"pith:B2TZ7OFG","schema_version":"1.0","canonical_sha256":"0ea79fb8a68daf3caf7cf2de884040faf6d0b02166af4cb103999015e97ba03f","source":{"kind":"arxiv","id":"2110.02479","version":1},"attestation_state":"computed","paper":{"title":"Exponentially Many Local Minima in Quantum Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"quant-ph","authors_text":"Xiaodi Wu, Xuchen You","submitted_at":"2021-10-06T03:23:44Z","abstract_excerpt":"Quantum Neural Networks (QNNs), or the so-called variational quantum circuits, are important quantum applications both because of their similar promises as classical neural networks and because of the feasibility of their implementation on near-term intermediate-size noisy quantum machines (NISQ). However, the training task of QNNs is challenging and much less understood. We conduct a quantitative investigation on the landscape of loss functions of QNNs and identify a class of simple yet extremely hard QNN instances for training. Specifically, we show for typical under-parameterized QNNs, ther"},"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":"2110.02479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-10-06T03:23:44Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"911e5830cd803b3488b5e613f1786e311c81bb67623851b99d156fc00a7288ca","abstract_canon_sha256":"a7091d706a3bfe12f6035d1650bcf07cc1735580cd50011b932cd4d83b8e0698"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:20:26.616016Z","signature_b64":"wY/34HFL4kd1/RUuqpZzAAhlaErWSex6BxZidJS8STfr2oR4Xyh+YnA1obFYtQ8HxgVqanS7n0ifyn33a/CSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ea79fb8a68daf3caf7cf2de884040faf6d0b02166af4cb103999015e97ba03f","last_reissued_at":"2026-07-05T03:20:26.615596Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:20:26.615596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponentially Many Local Minima in Quantum Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"quant-ph","authors_text":"Xiaodi Wu, Xuchen You","submitted_at":"2021-10-06T03:23:44Z","abstract_excerpt":"Quantum Neural Networks (QNNs), or the so-called variational quantum circuits, are important quantum applications both because of their similar promises as classical neural networks and because of the feasibility of their implementation on near-term intermediate-size noisy quantum machines (NISQ). However, the training task of QNNs is challenging and much less understood. We conduct a quantitative investigation on the landscape of loss functions of QNNs and identify a class of simple yet extremely hard QNN instances for training. Specifically, we show for typical under-parameterized QNNs, ther"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.02479","kind":"arxiv","version":1},"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/2110.02479/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":"2110.02479","created_at":"2026-07-05T03:20:26.615653+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.02479v1","created_at":"2026-07-05T03:20:26.615653+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.02479","created_at":"2026-07-05T03:20:26.615653+00:00"},{"alias_kind":"pith_short_12","alias_value":"B2TZ7OFGRWXT","created_at":"2026-07-05T03:20:26.615653+00:00"},{"alias_kind":"pith_short_16","alias_value":"B2TZ7OFGRWXTZL34","created_at":"2026-07-05T03:20:26.615653+00:00"},{"alias_kind":"pith_short_8","alias_value":"B2TZ7OFG","created_at":"2026-07-05T03:20:26.615653+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.09988","citing_title":"Absence of poor local minima in matrix product states","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2606.09988","citing_title":"Absence of poor local minima in matrix product states","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2606.05719","citing_title":"Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the $(1+1)$d $\\mathbb{Z}_2$ lattice gauge theory","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2606.28483","citing_title":"Quantum Fourier Generative Models Trainable at Large Scale","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2604.16701","citing_title":"Enabling Lie-Algebraic Classical Simulation beyond Free Fermions","ref_index":71,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L","json":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L.json","graph_json":"https://pith.science/api/pith-number/B2TZ7OFGRWXTZL346LPIQQCA7L/graph.json","events_json":"https://pith.science/api/pith-number/B2TZ7OFGRWXTZL346LPIQQCA7L/events.json","paper":"https://pith.science/paper/B2TZ7OFG"},"agent_actions":{"view_html":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L","download_json":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L.json","view_paper":"https://pith.science/paper/B2TZ7OFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.02479&json=true","fetch_graph":"https://pith.science/api/pith-number/B2TZ7OFGRWXTZL346LPIQQCA7L/graph.json","fetch_events":"https://pith.science/api/pith-number/B2TZ7OFGRWXTZL346LPIQQCA7L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L/action/storage_attestation","attest_author":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L/action/author_attestation","sign_citation":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L/action/citation_signature","submit_replication":"https://pith.science/pith/B2TZ7OFGRWXTZL346LPIQQCA7L/action/replication_record"}},"created_at":"2026-07-05T03:20:26.615653+00:00","updated_at":"2026-07-05T03:20:26.615653+00:00"}