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Paper Citation Record · LEDGER

Better product formulas for quantum phase estimation

As of 15 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2412.16811.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.16811 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T10:29:18.166260Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

21 of 21 outbound references displayed

  • verified exact0
  • verified fuzzy7
  • unresolved14
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a2a39336-c6e4-42eb-a77f-07775c47f147 · outbound

This paper cites This is because the lowest contribution comes from the first term above 1 s R s 0 dσE(σ), where we recall E(σ) = O(σp).

Better product formulas for quantum phase estimation This is because the lowest contribution comes from the first term above 1 s R s 0 dσE(σ), where we recall E(σ) = O(σp)

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:29:18.370359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.091448Z digest=sha256:af10c187a59c4f37eab6851f0947b515ece3276e90cf887ea5b6a386e105251d

Observation a3c441dc-eda7-48a4-b33b-2139ffbb8258 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 2

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unresolved
raw_fallback, observed 2026-08-11T10:29:18.359944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.095876Z digest=sha256:8a3645e6bada80abd9e882073e46313a0106b52d2724173374ad30302db2373e

Observation b101349f-b3f4-4ed5-a9ee-a24330c6a9bd · outbound

This paper cites (4) up to (but not including) order s2p+1, only the term 1 s R s 0 dσ ⟨ψ|E(σ)|ψ⟩ contributes.

Better product formulas for quantum phase estimation (4) up to (but not including) order s2p+1, only the term 1 s R s 0 dσ ⟨ψ|E(σ)|ψ⟩ contributes

Reference 3

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verified fuzzy
raw_fallback, observed 2026-08-11T10:29:18.350855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.099433Z digest=sha256:b651c2c7845c7f084f29b0f8b00d46e7c57a68a376bee9a0186d17440e2f8823

Observation 242a3b69-f1fa-4b06-84b4-28a8daffe9b3 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 4

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raw_fallback, observed 2026-08-11T10:29:18.340279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.103076Z digest=sha256:e67b27162ec6977bdfbade7983d613eb41fe81be40cb12568f646c4bcf10a16d

Observation e12432b5-3c1a-4502-87da-6dba297348de · outbound

This paper cites Lloyd, Science 273, 1073 (1996).

Better product formulas for quantum phase estimation Lloyd, Science 273, 1073 (1996)

Reference 5

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.107288Z digest=sha256:7dbfd0cb0279adb13ef30a1b07b78ff1c681926945abf3f2abc798d19e26e8be

Observation 3ed98c8c-f51c-45c4-9a47-34d2fa47e683 · outbound

This paper cites Suzuki, Journal of Mathematical Physics 32, 400 (1991).

Better product formulas for quantum phase estimation Suzuki, Journal of Mathematical Physics 32, 400 (1991)

Reference 6

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no resolver link, observed 2026-08-11T10:29:18.111218Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.111218Z digest=sha256:1a1aa9fb79e8b7466edfd444db803fca8ef58e2953929100ad4b19a79e77c7a2

Observation 043d8316-fe81-4fc9-9f73-6345c3988973 · outbound

This paper cites Campbell, Physical review letters 123, 070503 (2019).

Better product formulas for quantum phase estimation Campbell, Physical review letters 123, 070503 (2019)

Reference 7

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verified fuzzy
raw_fallback, observed 2026-08-11T10:29:18.319081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.115805Z digest=sha256:2592f068801a464c9a27fd644697d57d5aaf6c6ce2752b7eaecfabebcf98ef21

Observation 2b96d95d-1d67-47eb-803f-1d84338996e8 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 8

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unresolved
raw_fallback, observed 2026-08-11T10:29:18.307675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.119072Z digest=sha256:4fd0330c2432be75f6f9b226fa7781b292f102b60a06918b2d56e218e02c745c

Observation 018d2f0b-4bd3-4da3-b0ed-4d480f5a06e4 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-11T10:29:18.297109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.123594Z digest=sha256:39a188b96c25daaa52dad4e765d29b7e9fa41cd80c68880c9bb3d52125ecab58

Observation 31decccf-dbe6-421b-91f9-7ceced6cdb76 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-11T10:29:18.127852Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.127852Z digest=sha256:08ff4a1a7f9de5014c3ab38067816edb747ff803370c121c105f76549686f0ec

Observation 72e11734-c9fd-480c-934d-cbe1920b526e · outbound

This paper cites Well-conditioned multiproduct Hamiltonian simulation.

Better product formulas for quantum phase estimation Well-conditioned multiproduct Hamiltonian simulation

Reference 11

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.130994Z digest=sha256:bff4239778d2515feda7a92c3f9abc86ea69ca02727c24344dd246c4777ac69d

Observation 9cc97eb5-834d-44f5-bcc5-84c3ea603db9 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 12

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unresolved
no resolver link, observed 2026-08-11T10:29:18.134540Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.134540Z digest=sha256:346078de705c959fb388a24de6e20f179348821a31c214a1757fbe2e08c6cce8

Observation 3c7b28a1-e52c-4f73-82d0-f5c0402fee1b · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 13

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unresolved
no resolver link, observed 2026-08-11T10:29:18.137790Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.137790Z digest=sha256:4f34d6891a1016e305e49bcd5c165604d756ca13c582e1ba87c21d7b7fb07816

Observation f19532f2-09b5-4a2f-bd30-d8a0068fb290 · outbound

This paper cites Yi and E.

Better product formulas for quantum phase estimation Yi and E

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:29:18.269593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.140341Z digest=sha256:ee9989725ff68ee7e81f011697296006a211307bbac97b1b331da4ecb9fcec69

Observation 3c274a52-4988-4330-b12a-5604f29c4f37 · outbound

This paper cites S ¸ahino˘ glu and R.

Better product formulas for quantum phase estimation S ¸ahino˘ glu and R

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:29:18.259653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 93d86578-ed4b-4054-8a06-2a4cb9698b90 · outbound

This paper cites Better bounds for low-energy product formulas.

Better product formulas for quantum phase estimation Better bounds for low-energy product formulas

Reference 16

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unresolved
no resolver link, observed 2026-08-11T10:29:18.147840Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.147840Z digest=sha256:a01a7484608469d15ce876a901c0765adb2e7c91bb3a1f5405923879d6c16727

Observation a66ac19e-bba9-40e1-98be-824d905d7451 · outbound

This paper cites Blanes, F.

Better product formulas for quantum phase estimation Blanes, F

Reference 17

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unresolved
no resolver link, observed 2026-08-11T10:29:18.151615Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T10:29:18.151615Z digest=sha256:a4e7f66db72e2db3421311b369ce31624042aff0c7d1a3ac203e35b7b6d3708d

Observation c5c5b386-cfc8-40fa-ad1a-63105b251e90 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 18

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unresolved
raw_fallback, observed 2026-08-11T10:29:18.243875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.155419Z digest=sha256:e0ed9238079c815655f048b168a47786638a1a267591830a5660832585e8fe1e

Observation 5b467387-0f5f-4307-8e31-1085bcefbc23 · outbound

This paper cites Arnal, F.

Better product formulas for quantum phase estimation Arnal, F

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:29:18.233750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.159149Z digest=sha256:4a0e7b175ff369aec6eb1a3409d018f01d4b2780c0c9c7c2b9ea88925b93cd92

Observation 16b73f47-addc-48f3-b34b-52cad2a660c2 · outbound

This paper cites an unresolved cited work.

Better product formulas for quantum phase estimation Unresolved cited work

Reference 20

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unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T10:29:18.162770Z digest=sha256:744d851fe7f57b8d59f3a89460ee5eba4d8694271b0ea1ff7350919086bebd68

Observation 6dd7ce8a-7c15-43cc-a427-c1538cd0e9a6 · outbound

This paper cites Jansen, M.-B.

Better product formulas for quantum phase estimation Jansen, M.-B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T10:29:18.212271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Pith citing papers

No inbound Pith citation observations are available.