Paper Citation Record · LEDGER

Complexity phase transition for continuous-variable cluster state

As of 6 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2604.07804.

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

pith.paper-citation-record.v1
2604.07804 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T18:04:24.209217Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+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

40 of 40 outbound references displayed

verified exact2
verified fuzzy33
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0c4dcece-b5af-44ce-a4bc-6951c3279891 · outbound

This paper cites S5, thus obtaining the cluster state |GU ⟩ (with additional noise and displacement given in Eq.

Complexity phase transition for continuous-variable cluster state S5, thus obtaining the cluster state |GU ⟩ (with additional noise and displacement given in Eq

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.699725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation bfafdada-dd9a-4d6c-ba6a-f1194c912024 · outbound

This paper cites an unresolved cited work.

Complexity phase transition for continuous-variable cluster state Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-17T07:21:39.280777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation daa66540-ebec-41d0-bb4e-c2d6d1014d5e · outbound

This paper cites an unresolved cited work.

Complexity phase transition for continuous-variable cluster state Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-05-17T07:21:39.255431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 30c86f05-8845-4a2a-875c-904e869d32a9 · outbound

This paper cites Proof of Theorem 4.

Complexity phase transition for continuous-variable cluster state Proof of Theorem 4

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.718234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ebc55942-21bd-4016-8b34-a954fd8e0c35 · outbound

This paper cites By deﬁnition, GT =G⊐ ◦G⊐ ◦G⊐ and φ T = φ b ·φ a ·φ a.

Complexity phase transition for continuous-variable cluster state By deﬁnition, GT =G⊐ ◦G⊐ ◦G⊐ and φ T = φ b ·φ a ·φ a

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.290523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 986dfe46-2f54-4149-938e-32474a4f9cc9 · outbound

This paper cites an unresolved cited work.

Complexity phase transition for continuous-variable cluster state Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-17T07:21:39.259204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation be4db222-c149-428e-ba94-871e947a17af · outbound

This paper cites Based on the above arguments, we are ﬁnally ready to prove Lemma 1.

Complexity phase transition for continuous-variable cluster state Based on the above arguments, we are ﬁnally ready to prove Lemma 1

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.705068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 1543046e-90f2-4cfa-ab16-edc45e5891af · outbound

This paper cites Combining all these arguments, by Weyl’s inequa lity [17], the minimum eigenvalue of N(G(M) D , φ Tj )N(G(M) D , φ Tj )T is at least 6 − 4 √ 2.

Complexity phase transition for continuous-variable cluster state Combining all these arguments, by Weyl’s inequa lity [17], the minimum eigenvalue of N(G(M) D , φ Tj )N(G(M) D , φ Tj )T is at least 6 − 4 √ 2

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.229603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 15deb472-8675-40e4-85bd-f732332f6e6b · outbound

This paper cites Concatenation of graphs.

Complexity phase transition for continuous-variable cluster state Concatenation of graphs

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.263259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation dc8e2c62-37ef-4fcc-8f89-7af87561eb95 · outbound

This paper cites Universal quantum computation with continuous-variable cluster sta tes.

Complexity phase transition for continuous-variable cluster state Universal quantum computation with continuous-variable cluster sta tes

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.284379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 24880d55-4471-4533-b84f-ecfa6544dd13 · outbound

This paper cites Quantum computing with continuous-variable clusters.

Complexity phase transition for continuous-variable cluster state Quantum computing with continuous-variable clusters

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.726849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b135764f-56b7-4ffb-b781-5fbc9d413073 · outbound

This paper cites Noise analysis of single-mode gaussian operations using continuous-variable cluster states.

Complexity phase transition for continuous-variable cluster state Noise analysis of single-mode gaussian operations using continuous-variable cluster states

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.224201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 43a9020c-8d62-42e3-887e-7e709798461a · outbound

This paper cites Fault-tolerant measurement-based qu antum computing with continuous-variable cluster states.

Complexity phase transition for continuous-variable cluster state Fault-tolerant measurement-based qu antum computing with continuous-variable cluster states

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.731293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation e1e5d9a6-a673-480a-9983-32f27e79c966 · outbound

This paper cites Architecture and noise analysis of continuous-varia ble quantum gates using two-dimensional cluster states.

Complexity phase transition for continuous-variable cluster state Architecture and noise analysis of continuous-varia ble quantum gates using two-dimensional cluster states

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.243418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation bbe9973f-4769-4ebf-bf2f-80c32f5ffa4f · outbound

This paper cites Deterministic multi- mode gates on a scalable photonic quantum computing platfor m.

Complexity phase transition for continuous-variable cluster state Deterministic multi- mode gates on a scalable photonic quantum computing platfor m

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.252197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 3ade35d7-87fe-43bc-bcc6-3bf728794fdc · outbound

This paper cites Fault- tolerant continuous-variable measurement-based quantum computation architecture.

Complexity phase transition for continuous-variable cluster state Fault- tolerant continuous-variable measurement-based quantum computation architecture

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.226532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b5543aec-4fb7-4431-baca-11be09dcb33a · outbound

This paper cites Universal linear bogoliubov transformations through one-way quantum computation.

Complexity phase transition for continuous-variable cluster state Universal linear bogoliubov transformations through one-way quantum computation

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.232865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c83c2eb3-5918-44f6-a887-f4e47a95d136 · outbound

This paper cites Eﬃcient quantum pseudorandomness with simple graph states.

Complexity phase transition for continuous-variable cluster state Eﬃcient quantum pseudorandomness with simple graph states

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.267041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 21e9418c-31de-4b0e-8901-d8318035e58a · outbound

This paper cites Experimental realization of any discrete unit ary operator.

Complexity phase transition for continuous-variable cluster state Experimental realization of any discrete unit ary operator

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.293920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 60d9b2e9-0868-4700-9abc-8e3c84d6d02f · outbound

This paper cites Optimal design for universal multiport interferometers.

Complexity phase transition for continuous-variable cluster state Optimal design for universal multiport interferometers

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.198329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c9098bed-faac-4478-87eb-fbef161fbf62 · outbound

This paper cites Suﬃcient conditions for eﬃcient classical simulation of quantum optics.

Complexity phase transition for continuous-variable cluster state Suﬃcient conditions for eﬃcient classical simulation of quantum optics

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.205571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a6e603c8-0981-472b-94ed-d9457c032952 · outbound

This paper cites Some formal properties of the density matrix.

Complexity phase transition for continuous-variable cluster state Some formal properties of the density matrix

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.277452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 25531f4f-ac7a-4b09-8965-d6425c86fd82 · outbound

This paper cites Photon correlations.

Complexity phase transition for continuous-variable cluster state Photon correlations

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.248510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation f419aa82-6173-4872-b93a-50f533247c6d · outbound

This paper cites an unresolved cited work.

Complexity phase transition for continuous-variable cluster state Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-05-17T07:21:39.273775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation cd557ce0-705b-411c-aabd-d36a31719ffa · outbound

This paper cites Das asymptotische verteilungsgesetz der eig enwerte linearer partieller diﬀerentialgleichungen (mit einer anwendung auf die theorie der hohlraumstrahlung).

Complexity phase transition for continuous-variable cluster state Das asymptotische verteilungsgesetz der eig enwerte linearer partieller diﬀerentialgleichungen (mit einer anwendung auf die theorie der hohlraumstrahlung)

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.187674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 5d022a92-e8aa-4de6-ba72-6f162033a73e · outbound

This paper cites Gaussian boson sampling.

Complexity phase transition for continuous-variable cluster state Gaussian boson sampling

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.709572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 660f6dbc-54af-46be-a1b1-f7b5de0e8e83 · outbound

This paper cites Detailed study of gaussian boson sampling.

Complexity phase transition for continuous-variable cluster state Detailed study of gaussian boson sampling

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.299458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 32508b69-b7e1-4b50-b099-2c934cf13789 · outbound

This paper cites Quantum compu tational advantage via high-dimensional gaussian boson sampling.

Complexity phase transition for continuous-variable cluster state Quantum compu tational advantage via high-dimensional gaussian boson sampling

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.174663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 99a8be58-64b6-40c9-804e-604950378509 · outbound

This paper cites Suﬃcient co nditions for hardness of lossy gaussian boson sampling.

Complexity phase transition for continuous-variable cluster state Suﬃcient co nditions for hardness of lossy gaussian boson sampling

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:35:57.024588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 6b6844e1-da66-48f4-a665-325697710f27 · outbound

This paper cites Uhlmann ﬁdelity between t wo-mode gaussian states.

Complexity phase transition for continuous-variable cluster state Uhlmann ﬁdelity between t wo-mode gaussian states

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.685097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a6f30f75-e8c9-4e49-9815-1988aed993ef · outbound

This paper cites A limit formula for the quantum ﬁdelity.

Complexity phase transition for continuous-variable cluster state A limit formula for the quantum ﬁdelity

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.178185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 83b61c70-1639-4dec-87e0-bb1545939cb6 · outbound

This paper cites Cryptographic d istinguishability measures for quantum-mechanical state s.

Complexity phase transition for continuous-variable cluster state Cryptographic d istinguishability measures for quantum-mechanical state s

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.191021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 4abfca8f-3167-43df-b55a-38153f55e02d · outbound

This paper cites Pp is as hard as the polynomial-time hierarc hy.

Complexity phase transition for continuous-variable cluster state Pp is as hard as the polynomial-time hierarc hy

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.202013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation d0ce5488-fd79-4a92-a4e0-caedecf0cba1 · outbound

This paper cites On approximation algorithms for# p.

Complexity phase transition for continuous-variable cluster state On approximation algorithms for# p

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.722632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 4299130d-f0e6-4b3f-98c3-18fa13bea9cb · outbound

This paper cites A linear-optical proof that the permanent i s# p-hard.

Complexity phase transition for continuous-variable cluster state A linear-optical proof that the permanent i s# p-hard

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.296368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ee383dff-7228-4f98-8845-80aded4285ac · outbound

This paper cites Exponential improvements to the average-case hardness of BosonSampling.

Complexity phase transition for continuous-variable cluster state Exponential improvements to the average-case hardness of BosonSampling

Reference 36

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T05:35:57.034065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 5ce9a15a-777a-4b2a-8940-0fce28cdeb59 · outbound

This paper cites The computational comple xity of linear optics.

Complexity phase transition for continuous-variable cluster state The computational comple xity of linear optics

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.270636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a4ec6d37-b448-4682-9fde-bd753dbb3e0b · outbound

This paper cites Hafnian of two-parameter matrices.

Complexity phase transition for continuous-variable cluster state Hafnian of two-parameter matrices

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-05-11T05:35:57.012512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation ec92b66e-5ce2-42fd-8bdc-46ac7d217103 · outbound

This paper cites Transforming graph sta tes using single-qubit operations.

Complexity phase transition for continuous-variable cluster state Transforming graph sta tes using single-qubit operations

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:24:13.713924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 18d2030e-4dbb-453a-888d-b038439c59e9 · outbound

This paper cites Complexity phase transitions generated by entanglement.

Complexity phase transition for continuous-variable cluster state Complexity phase transitions generated by entanglement

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T07:21:39.287457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Pith citing papers

No inbound Pith citation observations are available.