Paper Citation Record · LEDGER

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex

As of 12 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2608.11173.

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

pith.paper-citation-record.v1
2608.11173 v1

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T04:54:20.264665Z

measured 42 of 42 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

42 of 42 outbound references displayed

verified exact0
verified fuzzy28
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ace19556-60fc-40a0-8db2-8d6d829f92ce · outbound

This paper cites Gomez, Lukasz Kaiser, and Illia Polosukhin.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Gomez, Lukasz Kaiser, and Illia Polosukhin

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.727588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6f2f8a30-6191-4976-844a-fda797466d4a · outbound

This paper cites Deep residual learning for im- age recognition.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Deep residual learning for im- age recognition

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-12T04:54:20.125848Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d5a45df-ce71-404f-9d59-065a86bf2da9 · outbound

This paper cites Highway networks, 2015.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Highway networks, 2015

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.709741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5f1ad7bd-e747-4e67-b681-cca3b6db08ad · outbound

This paper cites Rethinking attention with Performers.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Rethinking attention with Performers

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.699461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a90f7ae2-1b22-4dba-80c9-d1b1464afdb9 · outbound

This paper cites Transformer dissection: An unified understanding for transformer’s attention via the lens of kernel.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Transformer dissection: An unified understanding for transformer’s attention via the lens of kernel

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.688996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1c47f09e-d789-4390-aa7e-c2a710ac3abf · outbound

This paper cites Quantum Science and Technology.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum Science and Technology

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.678132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 912fa03a-26fc-4694-adf6-cd2d73794cc7 · outbound

This paper cites Bromley, Juan Miguel Arrazola, Soran Jahangiri, Josh Izaac, Nicol´ as Quesada, Alain Delgado Gran, Maria Schuld, Jeremy Swinarton, Zeid Zabaneh, and Nathan Killoran.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Bromley, Juan Miguel Arrazola, Soran Jahangiri, Josh Izaac, Nicol´ as Quesada, Alain Delgado Gran, Maria Schuld, Jeremy Swinarton, Zeid Zabaneh, and Nathan Killoran

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.667548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 598638b5-61a6-4861-8376-2a199d0a4613 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-12T04:54:20.148564Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aceadbc2-7406-4a48-94df-7ba6df840dd1 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-12T04:54:20.151903Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06185091-0fb9-4c3e-8482-733d1fc42baa · outbound

This paper cites Dirichlet flow matching with applications to DNA sequence design, 2024.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Dirichlet flow matching with applications to DNA sequence design, 2024

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.643754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 27633a6f-c6e9-4987-a836-7271618e284b · outbound

This paper cites Richemond, Arnaud Doucet, Robin Strudel, Chris Dyer, Conor Durkan, Curtis Hawthorne, R´ emi Leblond, Will Grathwohl, and Jonas Adler.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Richemond, Arnaud Doucet, Robin Strudel, Chris Dyer, Conor Durkan, Curtis Hawthorne, R´ emi Leblond, Will Grathwohl, and Jonas Adler

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.633255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5a41c5cd-96f9-4130-a2df-ccc41dcaa5d6 · outbound

This paper cites Quantum vision transformers.Quantum, 8:1265, 2024.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum vision transformers.Quantum, 8:1265, 2024

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.621573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 46425aed-df15-445b-bfe4-bc5a8f082f7f · outbound

This paper cites QSAN: A near- term achievable quantum self-attention network, 2022.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex QSAN: A near- term achievable quantum self-attention network, 2022

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.609580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e4049664-f14c-4987-abd6-b83bb35dcb24 · outbound

This paper cites Quantum complex-valued self-attention model, 2025.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum complex-valued self-attention model, 2025

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.598511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 70f0b305-9ba1-46dd-9311-72423d7cc7bd · outbound

This paper cites Quantum transformer: Accelerating model inference via quantum linear algebra, 2024.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum transformer: Accelerating model inference via quantum linear algebra, 2024

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.587971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1ff1220c-b809-41b4-a691-9728490268bc · outbound

This paper cites Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.576216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4c05eba2-fc19-4b3b-8640-11c4a35b9241 · outbound

This paper cites Childs, Robin Kothari, and Rolando D.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Childs, Robin Kothari, and Rolando D

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-12T04:54:20.179757Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba57c637-e26c-4cf0-a9b6-1b25ee5cbc9a · outbound

This paper cites Childs and Nathan Wiebe.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Childs and Nathan Wiebe

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.557495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation efec8536-137b-499a-ba7d-2b13ed8b7048 · outbound

This paper cites The Lean 4 theorem prover and programming language.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex The Lean 4 theorem prover and programming language

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T04:54:20.186663Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42beadb4-99e0-4cfa-936f-7775a1d06602 · outbound

This paper cites The Lean mathematical library.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex The Lean mathematical library

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.539001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 829b62eb-e9a7-40aa-9ea7-3c5ef16310fc · outbound

This paper cites Bennett, Richard Cleve, David P.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Bennett, Richard Cleve, David P

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.528892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7e899257-959d-4ee8-a839-c987cbfb7c9e · outbound

This paper cites Bremner, Christopher M.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Bremner, Christopher M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.518325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e0638ec0-b336-4fce-b663-5f5a0c85fceb · outbound

This paper cites The effect of data encoding on the expressive power of variational quantum machine learning models.Physical Review A, 103(3):032430, 2021.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex The effect of data encoding on the expressive power of variational quantum machine learning models.Physical Review A, 103(3):032430, 2021

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.507136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3af1a197-c6f8-4894-93e4-7a824feb114a · outbound

This paper cites Shende, Stephen S.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Shende, Stephen S

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.496538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a6f6a2ef-de73-4219-b5cd-85aded2c437d · outbound

This paper cites Quantum fingerprinting.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum fingerprinting

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.486440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 87312777-934c-4275-be54-bd52f62babf1 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:54:20.475367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1518b8b6-9824-4bae-809b-ed163aae11d1 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:54:20.465336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b0c86a21-66de-4256-ad0d-6526c8592960 · outbound

This paper cites Wiseman and Gerard J.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Wiseman and Gerard J

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-12T04:54:20.217965Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6ede823-687d-410f-ac22-4b39affdf019 · outbound

This paper cites Fowler, Matteo Mariantoni, John M.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Fowler, Matteo Mariantoni, John M

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.447697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2c4830f0-7a39-4ac9-9f7c-80c6aa691448 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:54:20.437294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 14ee649f-3fbe-4b0b-a744-196b41d7172c · outbound

This paper cites Universal quantum computation with ideal Clifford gates and noisy ancillas.Physical Review A, 71(2):022316, 2005.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Universal quantum computation with ideal Clifford gates and noisy ancillas.Physical Review A, 71(2):022316, 2005

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.426640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 11425c2e-e680-4e60-ab4f-393425adab8e · outbound

This paper cites Quantum amplitude amplifi- cation and estimation.Contemporary Mathematics, 305:53–74, 2002.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum amplitude amplifi- cation and estimation.Contemporary Mathematics, 305:53–74, 2002

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.416362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 25a55880-255e-4e0c-804e-217d4d282498 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:54:20.405721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c547affe-dc5d-456c-8cfe-f9e50d1d50e6 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:54:20.393622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b16c1df1-fa64-45fc-8916-7c00aa602b26 · outbound

This paper cites Quantum random access memory.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Quantum random access memory

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.380458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d8dbe7cb-36b4-4908-ba51-718694da5764 · outbound

This paper cites Yoder, Guang Hao Low, and Isaac L.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Yoder, Guang Hao Low, and Isaac L

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.367299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3f53452c-9fdf-41b1-aeb3-9925fcc4bb01 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:54:20.355237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation efc781b9-db23-4860-ba90-294218ef4f47 · outbound

This paper cites Correia, Vlad Niculae, and Andr´ e F.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Correia, Vlad Niculae, and Andr´ e F

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.342204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1f460980-aa85-489d-a4c2-cf36c8909e74 · outbound

This paper cites an unresolved cited work.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-12T04:54:20.329150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3d3a5ff8-2667-4bb6-b5d5-1b84c6f74157 · outbound

This paper cites Dauphin, Angela Fan, Michael Auli, and David Grangier.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Dauphin, Angela Fan, Michael Auli, and David Grangier

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.317113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bbd66167-cbd1-4ce0-8a46-d59c257787f7 · outbound

This paper cites McClean, Sergio Boixo, Vadim N.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex McClean, Sergio Boixo, Vadim N

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-12T04:54:20.261350Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7f746b5-45ac-4764-b4ce-05f089812564 · outbound

This paper cites Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J.

A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T04:54:20.295711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.