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In other words, they exhibited a search problem in QNC^0 that is not in NC^0.\n  We strengthen their result by proving that the 2D HLF problem is not contained in AC^0, the class of classical, polynomial-size, constant-depth cir"},"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":"1906.08890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-06-20T22:53:06Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"cf17e9e7bb9d16380154416d890b3ef98cfca8c6d5628d5e29052eecae791976","abstract_canon_sha256":"22a40ed5f0c4bc597c4dc601e3af11aa675d36811ad8cf8b64fb4bd742cc8116"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:47.524736Z","signature_b64":"lXX+kcdEM8nfxx5iI73/PJJ6oOoCH+7wmGOwO26RdakoYnYUcn0SYF9pY4guvJGjdO6ZbXVKdElVVyjqW5hCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b47198bebe773286634456a18762cafa0cd103ce24b6fc1f42c4f6400a4b9931","last_reissued_at":"2026-05-17T23:42:47.524164Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:47.524164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Adam Bene Watts, Avishay Tal, Luke Schaeffer, Robin Kothari","submitted_at":"2019-06-20T22:53:06Z","abstract_excerpt":"Recently, Bravyi, Gosset, and K\\\"{o}nig (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth quantum circuit using bounded fan-in gates (or QNC^0 circuits), but cannot be solved by any constant-depth classical circuit using bounded fan-in AND, OR, and NOT gates (or NC^0 circuits). 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