Paper Citation Record · LEDGER

Invariants in Linear Optics

As of 22 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2509.02211.

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

pith.paper-citation-record.v1
2509.02211 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:58:17.861583Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T20:41:53.557398Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T01:09:18.818026Z

Reference resolution

29 of 29 outbound references displayed

verified exact2
verified fuzzy20
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 31f07d62-ece8-4b49-90e6-7761e70a9acb · outbound

This paper cites Review article: Linear optical quantum computing.

Invariants in Linear Optics Review article: Linear optical quantum computing

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T11:58:15.753949Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a95e9604-13f9-495e-adca-6bb306d2baf8 · outbound

This paper cites Photonic Quantum Computers.

Invariants in Linear Optics Photonic Quantum Computers

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T11:58:15.816838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b280e96-067a-4d14-8719-7a9ddda0dd74 · outbound

This paper cites A spin-optical quantum computing architecture,.

Invariants in Linear Optics A spin-optical quantum computing architecture,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:22.662646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 22daaa3f-a021-4119-a665-802b7ef68f1d · outbound

This paper cites Enhanced fault-tolerance in photonic quantum computing: Floquet code outperforms surface code in tailored architecture,.

Invariants in Linear Optics Enhanced fault-tolerance in photonic quantum computing: Floquet code outperforms surface code in tailored architecture,

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-05T11:58:15.931044Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 439e46f2-ac1d-4654-a2e6-fdae6ff9c87a · outbound

This paper cites Fusion-based quantum computation,.

Invariants in Linear Optics Fusion-based quantum computation,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:22.647231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8b1dc053-4c55-4685-ae18-f9f8f8c95424 · outbound

This paper cites Re- cent progress in quantum photonic chips for quantum communication and internet,.

Invariants in Linear Optics Re- cent progress in quantum photonic chips for quantum communication and internet,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:22.631086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5a8a24a5-a5aa-455c-ac95-1b07f985de5f · outbound

This paper cites A versatile single- photon-based quantum computing platform,.

Invariants in Linear Optics A versatile single- photon-based quantum computing platform,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:22.614484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7c5e306f-79f0-4b3d-8116-4dcff821941a · outbound

This paper cites A scheme for efficient quantum computation with linear optics,.

Invariants in Linear Optics A scheme for efficient quantum computation with linear optics,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:22.366904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 293d845e-ffe7-47e3-b4c5-223c3a08889d · outbound

This paper cites Quantum gates using linear optics and postselection,.

Invariants in Linear Optics Quantum gates using linear optics and postselection,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:22.133413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 71602663-0e87-4099-84b2-cc12a02916f4 · outbound

This paper cites Efficient toffoli gates using qudits,.

Invariants in Linear Optics Efficient toffoli gates using qudits,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:21.909916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dc5afd0d-522d-4851-b8e9-d0dc83ce120e · outbound

This paper cites A method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe.

Invariants in Linear Optics A method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:58:18.217986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 888e2425-72d7-450c-85e8-a3f77733527f · outbound

This paper cites Linear optics quantum computing - con- struction of small networks and asymptotic scaling,.

Invariants in Linear Optics Linear optics quantum computing - con- struction of small networks and asymptotic scaling,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:21.685770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 34dfa715-9009-4f8c-aed9-5d45483bbdbe · outbound

This paper cites Simple rules for two-photon state preparation with linear optics,.

Invariants in Linear Optics Simple rules for two-photon state preparation with linear optics,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:20.988247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3ac2f2da-a44a-4f06-aa99-22409fa9b238 · outbound

This paper cites No-go theorems for photon state transformations in quantum linear optics,.

Invariants in Linear Optics No-go theorems for photon state transformations in quantum linear optics,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:20.693389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6762ccd1-9a85-4080-9848-69e4c2184913 · outbound

This paper cites Sturmfels, Algorithms in Invariant Theory , ser.

Invariants in Linear Optics Sturmfels, Algorithms in Invariant Theory , ser

Reference 15

Resolution: verified exact; doi, observed 2026-08-05T11:58:18.045628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d4282e34-8b90-4a90-ae3a-f67d474fe267 · outbound

This paper cites An introduction to invariants and moduli,.

Invariants in Linear Optics An introduction to invariants and moduli,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:20.425928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 91dab127-2334-404d-ad68-afb3086f8795 · outbound

This paper cites Derksen and G.

Invariants in Linear Optics Derksen and G

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T11:58:17.023396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 770a2f5e-825c-49a2-89a3-dd0bc9797814 · outbound

This paper cites Dolgachev, Lectures on Invariant Theory , ser.

Invariants in Linear Optics Dolgachev, Lectures on Invariant Theory , ser

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:20.124171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ba167999-336a-4e75-ac3c-57640e83b0cf · outbound

This paper cites an unresolved cited work.

Invariants in Linear Optics Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-05T11:58:17.209249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69cdf256-fadf-4d04-a05c-76abf40a425a · outbound

This paper cites Integration with respect to the haar measure on unitary, orthogonal and symplectic group,.

Invariants in Linear Optics Integration with respect to the haar measure on unitary, orthogonal and symplectic group,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:19.941018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 48d2e68b-2e45-4810-b53d-0d25661ea3d8 · outbound

This paper cites Ueber die theorie der algebraischen formen,.

Invariants in Linear Optics Ueber die theorie der algebraischen formen,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:19.739966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 61c1e468-7ebb-4af7-bcd9-f8dccf42e941 · outbound

This paper cites The noether number in invariant theory.

Invariants in Linear Optics The noether number in invariant theory

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:19.495350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 206b33d7-cb52-44b5-8a5f-f9768309c31f · outbound

This paper cites Polynomial bounds for rings of invariants,.

Invariants in Linear Optics Polynomial bounds for rings of invariants,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:19.325569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 708bc73e-e6ff-4ed9-9dca-43b488a6757d · outbound

This paper cites On the castelnuovo-mumford regularity of rings of polynomial invariants,.

Invariants in Linear Optics On the castelnuovo-mumford regularity of rings of polynomial invariants,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:19.141928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c7a82ffe-832f-4f31-8029-73c72836d678 · outbound

This paper cites Molien, ¨Uber die Invarianten der linearen Substitutionsgruppen , ser.

Invariants in Linear Optics Molien, ¨Uber die Invarianten der linearen Substitutionsgruppen , ser

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:18.911376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5f385b97-b362-44b6-8cbc-f25112817779 · outbound

This paper cites Invariant polynomials and molien functions,.

Invariants in Linear Optics Invariant polynomials and molien functions,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:18.788964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f3fef21f-148a-4380-8e92-7a5747177ac5 · outbound

This paper cites an unresolved cited work.

Invariants in Linear Optics Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:58:18.658596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ddc30dde-77a5-4023-a96d-dde12e560af9 · outbound

This paper cites an unresolved cited work.

Invariants in Linear Optics Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:58:18.497759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 22057744-2afa-4225-97b0-b4b791cb5f9d · outbound

This paper cites Available: https://www.semanticscholar.org/ paper/Linear-optics-quantum-computing-construction-of-and-Kieling/ 11490cfeb0c2f5efca748d836c2c6f2f025540a3.

Invariants in Linear Optics Available: https://www.semanticscholar.org/ paper/Linear-optics-quantum-computing-construction-of-and-Kieling/ 11490cfeb0c2f5efca748d836c2c6f2f025540a3

Reference 2008

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:58:21.332705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation 39d9d543-6280-4a9f-ad18-2e38f6bbdd56 · inbound

Local controllability of heralded quantum linear optics cites this paper.

Local controllability of heralded quantum linear optics Invariants in Linear Optics

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-04T01:09:18.819653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.