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Paper Citation Record · LEDGER

Randomized product formulas beyond optimal deterministic scaling

As of 18 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 0 inbound Pith citation observations for arXiv:2608.07720.

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

pith.paper-citation-record.v1
2608.07720 v1

Coverage vector

measured 58 of 58 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:37:58.325168Z

measured 58 of 58 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

58 of 58 outbound references displayed

  • verified exact3
  • verified fuzzy11
  • unresolved43
  • parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 83ddb542-7dd3-4850-9bb2-63950b1819ed · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 1

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Unavailable: canonical work link unavailable.

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Observation 639e24b7-dfba-436d-86fc-6ed875abfcb4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 2

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Observation 10d10dab-15af-4c9a-8fe6-09eb3f0c9e9f · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 3

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Observation acf4d276-427d-4ab7-a06d-aa85643aa321 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 4

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Observation 413abaf2-da8d-430e-a9c5-6a453e2c69bd · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 5

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Observation 58694c73-db10-4db7-8319-7139405419f0 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 6

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Observation 589f638a-5ae5-47d8-a2ac-4d795084f733 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 7

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Observation a059ee98-c774-4d1e-85b1-cdcf439ff52e · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 8

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Observation 7485708e-b072-4816-b118-1d2b2d926d35 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 9

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Observation 0c10dcdf-74dc-4406-b36d-7a5a7b5eddac · outbound

This paper cites Suzuki, Fractal decomposition of exponential opera- tors with applications to many-body theories and monte carlo simulations, Physics Letters A146, 319 (1990).

Randomized product formulas beyond optimal deterministic scaling Suzuki, Fractal decomposition of exponential opera- tors with applications to many-body theories and monte carlo simulations, Physics Letters A146, 319 (1990)

Reference 10

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This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 11

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Observation e68ba28c-9526-46b0-bb36-c671d61d140b · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 12

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Observation d52080b5-9c28-4e60-ba7c-2f68eca463df · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 13

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Observation dd836807-5f45-4235-969e-91b11ae651ec · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 14

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Observation 89fe6523-4805-458e-ad5f-9561f265d73d · outbound

This paper cites Observation of separated dynamics of charge and spin in the Fermi-Hubbard model.

Randomized product formulas beyond optimal deterministic scaling Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Reference 15

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Observation 8a3dec34-73b0-423c-822a-eb339969ea42 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 16

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Observation dd1b66b5-0e0f-4040-aa31-453c8df60fd2 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 17

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 50162783-8c97-4141-a441-36cd78221986 · outbound

This paper cites Viola and E.

Randomized product formulas beyond optimal deterministic scaling Viola and E

Reference 18

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation d9e8b611-36da-4d75-85af-dc6ade4adf24 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 19

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 7059ea20-a584-4ebf-894f-3132d1bd32da · outbound

This paper cites Boixo, E.

Randomized product formulas beyond optimal deterministic scaling Boixo, E

Reference 20

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 723931aa-efb4-4435-9a14-972b4adb3bbc · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 21

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Observation 0d990e5d-aa34-49b2-a4ab-81b28ba8dd17 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 22

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Observation 1a419c82-df3e-4f96-bc72-fb8f237ac9d4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 23

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation bb792b6a-e5a5-4f08-a6b5-6f472d6e347d · outbound

This paper cites Gosset, R.

Randomized product formulas beyond optimal deterministic scaling Gosset, R

Reference 24

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Observation da7e6aa5-3f60-4ed5-8c6e-8fe6b45d05a3 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 25

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 2b9a48e9-4fb5-45f3-9902-da64a709b3a4 · outbound

This paper cites Randomized Quantum Optimal Control.

Randomized product formulas beyond optimal deterministic scaling Randomized Quantum Optimal Control

Reference 26

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation ba90f11b-ae84-4cf8-ac7f-43fff6a73162 · outbound

This paper cites G¨ unther, F.

Randomized product formulas beyond optimal deterministic scaling G¨ unther, F

Reference 27

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation d204c30b-bf9e-4085-906a-d0ac2444ff39 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 28

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Observation a76b01f7-a223-4ab0-bee9-b9bd816798eb · outbound

This paper cites Campbell, Random compiler for fast Hamiltonian sim- ulation, Physical Review Letters123, 070503 (2019).

Randomized product formulas beyond optimal deterministic scaling Campbell, Random compiler for fast Hamiltonian sim- ulation, Physical Review Letters123, 070503 (2019)

Reference 29

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Observation 9ee5bb7b-5af3-4482-8e9a-381c6a709ef6 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 30

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Observation db4a0308-c87c-4d0d-a77d-a718c48fa981 · outbound

This paper cites Ouyang, D.

Randomized product formulas beyond optimal deterministic scaling Ouyang, D

Reference 31

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source=pdf_text observed=2026-08-11T00:37:58.217130Z digest=sha256:b0183af7fc67b1c7eb6971db05df4d2dcb71a22a60cb5a952b17e144e584e264

Observation c50a7b2d-2c0b-455b-97bf-63e97a5a2f3e · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 32

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Observation fe407acf-9081-43d3-9f24-76a72f9b2774 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 33

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation af556f46-0510-45b1-b5ee-19725bfd6fad · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 34

Resolution
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raw_fallback, observed 2026-08-11T00:37:58.881562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 267a82b5-0f98-46fc-87ae-4de94c559381 · outbound

This paper cites Hamiltonian Simulation in the Interaction Picture.

Randomized product formulas beyond optimal deterministic scaling Hamiltonian Simulation in the Interaction Picture

Reference 35

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Source-reported events for the cited work

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Observation 49c59a1c-b8ee-4bff-8fed-00e16bddf049 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 36

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation c97852ff-a779-4365-a2d0-d7e6ba2036a9 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 37

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raw_fallback, observed 2026-08-11T00:37:58.859721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 594abc50-e50e-46b3-beb4-c9d682d1a4b7 · outbound

This paper cites Hamiltonian Simulation in the Interaction Picture Using the Magnus Expansion.

Randomized product formulas beyond optimal deterministic scaling Hamiltonian Simulation in the Interaction Picture Using the Magnus Expansion

Reference 38

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Observation 8bbb3504-17b7-452a-931a-ba72de6b22d4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 39

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source=pdf_text observed=2026-08-11T00:37:58.251200Z digest=sha256:9a1e6e03a36a0c787af79f809266d3b1785972438906f19cb1594b88ac372e8d

Observation f79cda87-80f7-4aab-8cbf-689ecf5369cf · outbound

This paper cites Bagherimehrab, L.

Randomized product formulas beyond optimal deterministic scaling Bagherimehrab, L

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.849289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.254952Z digest=sha256:9dc09e31d7f05156f88c26ca9ce0359354cb5612681e53ef4e96ee4a09132ef3

Observation a18af6eb-c652-4479-9210-4af470381d86 · outbound

This paper cites Watrous,The Theory of Quantum Information(Cam- bridge University Press, Cambridge, 2018).

Randomized product formulas beyond optimal deterministic scaling Watrous,The Theory of Quantum Information(Cam- bridge University Press, Cambridge, 2018)

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.258443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.258443Z digest=sha256:5ae3a904cf5dc1e7412738ca9ca5422058f53858d9142b57d29c44f970823628

Observation 8f298854-e2a4-4934-8f82-93c8fa7429e4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.261861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.261861Z digest=sha256:f7bd0cec75379abd489c45c4d1d3cefe3bc4a1d09ddabd6792b7dc92536dd22d

Observation 8ab3d686-b651-4f3d-b274-e146ba626025 · outbound

This paper cites Akibue, G.

Randomized product formulas beyond optimal deterministic scaling Akibue, G

Reference 43

Resolution
verified exact
doi, observed 2026-08-11T00:37:58.361386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.265207Z digest=sha256:225b85484f907d04c69025a33a9b5dae219515f30492d1a86c9f34b10608d7fe

Observation 35f82285-1cae-4384-baa8-bd00304d2996 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.825622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.268736Z digest=sha256:1434bba845f73adf67b20d3f88353bef18aad0fcd5619c090beb280b63f0c17c

Observation a6ce1f5b-f77c-4bef-86ee-b28727a73341 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 45

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.272538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.272538Z digest=sha256:e2d67bf4074373efd5de4c5053e7e8b99476cc33de4d8352d39845cc43e2646e

Observation 2781bc3d-88c8-487e-b8ec-4b13f738f442 · outbound

This paper cites Campbell, Shorter gate sequences for quantum com- puting by mixing unitaries, Physical Review A95, 042306 (2017).

Randomized product formulas beyond optimal deterministic scaling Campbell, Shorter gate sequences for quantum com- puting by mixing unitaries, Physical Review A95, 042306 (2017)

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.806633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.276384Z digest=sha256:6592e44ed271301794e21498b96d1a42d415765bdada1dfe87bf1b3ab28e7970

Observation d3bcb65e-f4f2-46d3-868a-aa45832b923a · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.280538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.280538Z digest=sha256:ed399a12496a0f00d736f7978f7ffe8dbcb76fc35f81e72d9caf4e48a210eedd

Observation e1ff6466-45ca-4516-bc71-26906451968f · outbound

This paper cites Chen, H.-Y.

Randomized product formulas beyond optimal deterministic scaling Chen, H.-Y

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.284269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.284269Z digest=sha256:fa88d1a60561e2127b59b9195e1361600a089e0a7e0b462700233a1b9e324620

Observation 0cd9511e-ae6d-4752-88d1-a74c32cd6c3c · outbound

This paper cites Kim and M.

Randomized product formulas beyond optimal deterministic scaling Kim and M

Reference 49

Resolution
verified exact
raw_fallback, observed 2026-08-11T00:37:58.465883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.288142Z digest=sha256:65f7146d9d8e292c6bf421ac04aa3d81e9f925f285a735e6dabf307c04d815a1

Observation 38fc3059-f490-4ea7-bbcc-5a841aee95ef · outbound

This paper cites Aharonov, A.

Randomized product formulas beyond optimal deterministic scaling Aharonov, A

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.778236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.291807Z digest=sha256:5e4cb14ad945543d1d72094d31817e6caf82786766ce5b29bb8a4d31c218e27a

Observation e1fc1071-020a-4d7c-a541-d14bf0e5a020 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.764671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.295798Z digest=sha256:61ad6485db99078085d074556649994af8b8bec5b20b3e0644226f2c7b95a8c7

Observation d01d8742-97df-4044-a616-ea2c354c6c96 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.751510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.300145Z digest=sha256:593a453453e7d16520c139d61e805ff7738ee3099f74d1c33a145f7e88c2a8f5

Observation b65f85c5-9848-41d9-9e93-6afc752c8458 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.738285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.304227Z digest=sha256:8f97ad440da278dda089375143dfab3bf30b7fd4a17d31c315005661324a5eac

Observation a6079df4-e209-40b9-838e-d082256d1dfd · outbound

This paper cites (28) 11 S3.3.

Randomized product formulas beyond optimal deterministic scaling (28) 11 S3.3

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.724425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.308215Z digest=sha256:ef1d24640c5d11bf5e2943a56fe7e57ec5f4d4f6c0944b6d9fb733d2a09bf10c

Observation bbe3815e-561e-4579-92bf-bc88c16412b0 · outbound

This paper cites The sampling distribution is chosen so that the averaged second-order 9 contribution of these corrections is the negative of the leadingα 2 error in Eq.

Randomized product formulas beyond optimal deterministic scaling The sampling distribution is chosen so that the averaged second-order 9 contribution of these corrections is the negative of the leadingα 2 error in Eq

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.710228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.313063Z digest=sha256:ccf76fae03e934fbb0e85c07a03a5281f26cea9270ddb260f4637026ce927227

Observation 469c6c0e-1869-42b6-9675-4f2dcb3bc310 · outbound

This paper cites For an explicit implementation, it is convenient to sample this distribution hierarchically rather than enumerate all tuples (a, b, n, q).

Randomized product formulas beyond optimal deterministic scaling For an explicit implementation, it is convenient to sample this distribution hierarchically rather than enumerate all tuples (a, b, n, q)

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.696164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.317280Z digest=sha256:9485d92a386893b60367181f60a98a3957b534e75b78d75dd6c70e6f534649ac

Observation 3fa63c04-1b07-4f4e-86c8-07c7e66d32c4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.682256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.321374Z digest=sha256:dd3f3d7bec1158dc76bd0369d5e8d3839c75c08d03e58bd5867b8fa2944ca891

Observation ae216321-c94c-410e-ac7b-4a58fbeed0b4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.669176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-11T00:37:58.325168Z digest=sha256:5152f8d2990eceee7967899955320ffcc4c9f559f23e9dd6c549e98dc2232c41

Pith citing papers

No inbound Pith citation observations are available.