{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PW6MQ3VKIWGI7J53RWPFA3F6QV","short_pith_number":"pith:PW6MQ3VK","canonical_record":{"source":{"id":"1503.06319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-21T16:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"412958ffcec2b973b818e47de76878192eae5c314532102db12283a9e2535505","abstract_canon_sha256":"75305c02a619c76e25849fcc4764587124f2ce0491c1a07583ae06e39740a19b"},"schema_version":"1.0"},"canonical_sha256":"7dbcc86eaa458c8fa7bb8d9e506cbe85514c804e49a8d0ffb612a8097a9d77fb","source":{"kind":"arxiv","id":"1503.06319","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06319","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06319v2","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06319","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"PW6MQ3VKIWGI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PW6MQ3VKIWGI7J53","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PW6MQ3VK","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PW6MQ3VKIWGI7J53RWPFA3F6QV","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-21T16:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"412958ffcec2b973b818e47de76878192eae5c314532102db12283a9e2535505","abstract_canon_sha256":"75305c02a619c76e25849fcc4764587124f2ce0491c1a07583ae06e39740a19b"},"schema_version":"1.0"},"canonical_sha256":"7dbcc86eaa458c8fa7bb8d9e506cbe85514c804e49a8d0ffb612a8097a9d77fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:40.010133Z","signature_b64":"B1uBzYWkPAPgywbA/GLRVnBb+jJWOChmbMEGfZ4Y2jfe2fJ1Zezae4NikJRPYWNSx+jr3zGLZ7Mgj6QKRbAWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dbcc86eaa458c8fa7bb8d9e506cbe85514c804e49a8d0ffb612a8097a9d77fb","last_reissued_at":"2026-05-18T01:09:40.009680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:40.009680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06319","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+7QTPy0P9z4poUBBmaw3hmcInGsED27BqX699SaXb+zsN4WRbrWYJXSpF/2r2J7vwNtyAjsfzsb1Z/SxDvvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:52:25.532737Z"},"content_sha256":"bac711bd046c0a1996a93a8b82fa53bee6027c6386c8241007b7aae9922c0285","schema_version":"1.0","event_id":"sha256:bac711bd046c0a1996a93a8b82fa53bee6027c6386c8241007b7aae9922c0285"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PW6MQ3VKIWGI7J53RWPFA3F6QV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum simulations of one dimensional quantum systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Rolando D. Somma","submitted_at":"2015-03-21T16:27:12Z","abstract_excerpt":"We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the quantum harmonic oscillator (QHO) based on a refined analysis of the Trotter-Suzuki formula that exploits the Lie algebra structure. For total evolution time $t$ and precision $\\epsilon>0$, the complexity of our method is $ O(\\exp(\\gamma \\sqrt{\\log(N/\\epsilon)}))$, where $\\gamma>0$ is a constant and $N$ is the quantum number associated with an \"energy cutoff\" of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06319","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIEBXRo3FU9kBHC21tB3wds5xii4o9X0q0xkWzClTwlFDylTvGrPpN/QyJwNqZsiwlo/QjDksEaRZuyh6QnXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:52:25.533112Z"},"content_sha256":"7dab34600d26257c808b323ede66754f9051ee347be800f4a7463a0c4329b69a","schema_version":"1.0","event_id":"sha256:7dab34600d26257c808b323ede66754f9051ee347be800f4a7463a0c4329b69a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PW6MQ3VKIWGI7J53RWPFA3F6QV/bundle.json","state_url":"https://pith.science/pith/PW6MQ3VKIWGI7J53RWPFA3F6QV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PW6MQ3VKIWGI7J53RWPFA3F6QV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T23:52:25Z","links":{"resolver":"https://pith.science/pith/PW6MQ3VKIWGI7J53RWPFA3F6QV","bundle":"https://pith.science/pith/PW6MQ3VKIWGI7J53RWPFA3F6QV/bundle.json","state":"https://pith.science/pith/PW6MQ3VKIWGI7J53RWPFA3F6QV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PW6MQ3VKIWGI7J53RWPFA3F6QV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PW6MQ3VKIWGI7J53RWPFA3F6QV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"75305c02a619c76e25849fcc4764587124f2ce0491c1a07583ae06e39740a19b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-21T16:27:12Z","title_canon_sha256":"412958ffcec2b973b818e47de76878192eae5c314532102db12283a9e2535505"},"schema_version":"1.0","source":{"id":"1503.06319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06319","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06319v2","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06319","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"PW6MQ3VKIWGI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PW6MQ3VKIWGI7J53","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PW6MQ3VK","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:7dab34600d26257c808b323ede66754f9051ee347be800f4a7463a0c4329b69a","target":"graph","created_at":"2026-05-18T01:09:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the quantum harmonic oscillator (QHO) based on a refined analysis of the Trotter-Suzuki formula that exploits the Lie algebra structure. For total evolution time $t$ and precision $\\epsilon>0$, the complexity of our method is $ O(\\exp(\\gamma \\sqrt{\\log(N/\\epsilon)}))$, where $\\gamma>0$ is a constant and $N$ is the quantum number associated with an \"energy cutoff\" of t","authors_text":"Rolando D. Somma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-21T16:27:12Z","title":"Quantum simulations of one dimensional quantum systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06319","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bac711bd046c0a1996a93a8b82fa53bee6027c6386c8241007b7aae9922c0285","target":"record","created_at":"2026-05-18T01:09:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"75305c02a619c76e25849fcc4764587124f2ce0491c1a07583ae06e39740a19b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-21T16:27:12Z","title_canon_sha256":"412958ffcec2b973b818e47de76878192eae5c314532102db12283a9e2535505"},"schema_version":"1.0","source":{"id":"1503.06319","kind":"arxiv","version":2}},"canonical_sha256":"7dbcc86eaa458c8fa7bb8d9e506cbe85514c804e49a8d0ffb612a8097a9d77fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dbcc86eaa458c8fa7bb8d9e506cbe85514c804e49a8d0ffb612a8097a9d77fb","first_computed_at":"2026-05-18T01:09:40.009680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:40.009680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B1uBzYWkPAPgywbA/GLRVnBb+jJWOChmbMEGfZ4Y2jfe2fJ1Zezae4NikJRPYWNSx+jr3zGLZ7Mgj6QKRbAWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:40.010133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bac711bd046c0a1996a93a8b82fa53bee6027c6386c8241007b7aae9922c0285","sha256:7dab34600d26257c808b323ede66754f9051ee347be800f4a7463a0c4329b69a"],"state_sha256":"e73f8b0f4ff472c421df20722df07d7b5769e869edb0e87db4cc72455a8d2cd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agoUhC6XnU14rKgbIEQ0ggPh9FixdoyvysSgtQCj+FF0STWTcFuaxmzpy3OeeRBJaThHEE0ibyVjM0YjL97nBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:52:25.536188Z","bundle_sha256":"10dc03a43d241923680ba79d8882c8e674f44f96b54105ff00b50a702b1dae04"}}