Paper Citation Record · LEDGER

Toward Minimum Graphic Parity Networks

As of 9 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2509.10070.

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

pith.paper-citation-record.v1
2509.10070 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T18:23:45.666129Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:55:26.692548Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T11:55:26.793514Z

Reference resolution

46 of 46 outbound references displayed

verified exact7
verified fuzzy0
unresolved35
parse uncertain0
malformed identifier4
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 542cd733-636c-484d-af27-b29f2136ada2 · outbound

This paper cites On the controlled-NOT com- plexity of controlled-NOT–phase circuits.Quantum Science and Technology, 4(1):015002, September 2018.doi:10.1088/2058-9565/aad8ca.

Toward Minimum Graphic Parity Networks On the controlled-NOT com- plexity of controlled-NOT–phase circuits.Quantum Science and Technology, 4(1):015002, September 2018.doi:10.1088/2058-9565/aad8ca

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:40.203809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 570ced5f-5c25-4c6d-8282-96736f454c5f · outbound

This paper cites Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations.

Toward Minimum Graphic Parity Networks Concentration Bounds for Quantum States and Limitations on the QAOA from Polynomial Approximations

Reference 2

Resolution: verified exact; doi, observed 2026-08-04T18:28:49.705340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0954f7c6-3fae-4d6a-bf13-1891703b3ab3 · outbound

This paper cites The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model.

Toward Minimum Graphic Parity Networks The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:40.387828Z

Source-reported events for the cited work

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Observation 3c79413a-449c-4284-a280-68fbcad9b429 · outbound

This paper cites Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models.

Toward Minimum Graphic Parity Networks Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:40.471893Z

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Observation e23d6311-8c0b-440d-a3bf-22ff17dff871 · outbound

This paper cites Cross, Jay M.

Toward Minimum Graphic Parity Networks Cross, Jay M

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:40.545464Z

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Observation d7b6ab62-7058-4df3-9b24-3c27b96405c7 · outbound

This paper cites Fixed-parameter tractability of graph modification problems for heredi- tary properties.Information Processing Letters, 58(4):171–176, 1996.

Toward Minimum Graphic Parity Networks Fixed-parameter tractability of graph modification problems for heredi- tary properties.Information Processing Letters, 58(4):171–176, 1996

Reference 6

Resolution: malformed identifier; no resolver link, observed 2026-08-04T18:23:40.629036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d266d33-133b-4134-ae97-311338ad4575 · outbound

This paper cites Generation of genuine entanglement up to 51 superconducting qubits.Nature, 619(7971):738–742, July 2023.doi:10.1038/s41586-023-06195-1.

Toward Minimum Graphic Parity Networks Generation of genuine entanglement up to 51 superconducting qubits.Nature, 619(7971):738–742, July 2023.doi:10.1038/s41586-023-06195-1

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:40.726399Z

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Observation 2a9b594e-4269-452c-9b8e-033b93aebcf5 · outbound

This paper cites Mémoire sur les nombres premiers.Journal de mathématiques pures et appliquées, Série 1:366–390, 1852.

Toward Minimum Graphic Parity Networks Mémoire sur les nombres premiers.Journal de mathématiques pures et appliquées, Série 1:366–390, 1852

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:40.897162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2934d131-9229-42b2-bcfa-52a2c1bb5c00 · outbound

This paper cites Faster and shorter synthesis of Hamiltonian simulation circuits.

Toward Minimum Graphic Parity Networks Faster and shorter synthesis of Hamiltonian simulation circuits

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.023414Z

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Observation 11d43e35-dc89-4714-92ae-a224e3ca21ee · outbound

This paper cites A Quantum Approximate Optimization Algorithm.

Toward Minimum Graphic Parity Networks A Quantum Approximate Optimization Algorithm

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.090006Z

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Observation b23f7d2e-e2ef-43b8-83a7-c34962d7438d · outbound

This paper cites Quantum Computation by Adiabatic Evolution.

Toward Minimum Graphic Parity Networks Quantum Computation by Adiabatic Evolution

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.139276Z

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Observation e79041f2-2882-4f3a-a873-11c059f16098 · outbound

This paper cites an unresolved cited work.

Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.288913Z

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Observation 3584ad27-6872-4e32-b78d-2940ff3cc870 · outbound

This paper cites Shallower cnot circuits on realistic quantum hardware.ACM Transactions on Quantum Computing, November 2024.

Toward Minimum Graphic Parity Networks Shallower cnot circuits on realistic quantum hardware.ACM Transactions on Quantum Computing, November 2024

Reference 13

Resolution: verified exact; doi, observed 2026-08-04T18:28:49.571422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f01e947e-df40-4673-873a-1a4adc30c3b9 · outbound

This paper cites Harrigan, Kevin J.

Toward Minimum Graphic Parity Networks Harrigan, Kevin J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.477005Z

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Observation a9f9b8dd-982a-42e2-ad81-5a4136b2205e · outbound

This paper cites Optimal space-depth trade-off of cnot circuits in quantum logic synthesis.

Toward Minimum Graphic Parity Networks Optimal space-depth trade-off of cnot circuits in quantum logic synthesis

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.642314Z

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Observation 2103af0f-97d7-49a1-a812-51eee1540c84 · outbound

This paper cites Algorithm 447: Efficient algorithms for graph manipula- tion.Communications of the ACM, June 1973.doi:10.1145/362248.362272.

Toward Minimum Graphic Parity Networks Algorithm 447: Efficient algorithms for graph manipula- tion.Communications of the ACM, June 1973.doi:10.1145/362248.362272

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.755218Z

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Observation b12cb121-2cba-409f-ba9d-d36993a5640d · outbound

This paper cites Exponential Quantum Space Ad- vantage for Approximating Maximum Directed Cut in the Streaming Model.

Toward Minimum Graphic Parity Networks Exponential Quantum Space Ad- vantage for Approximating Maximum Directed Cut in the Streaming Model

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:41.867610Z

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Observation 189b80b6-cf37-422e-a373-392b06664e02 · outbound

This paper cites Tractability of parameterized com- pletion problems on chordal, strongly chordal, and proper interval graphs.SIAM Journal on Computing, 28(5):1906–1922, 1999.

Toward Minimum Graphic Parity Networks Tractability of parameterized com- pletion problems on chordal, strongly chordal, and proper interval graphs.SIAM Journal on Computing, 28(5):1906–1922, 1999

Reference 18

Resolution: verified exact; doi, observed 2026-08-04T18:28:49.418766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 73b338dd-1793-4f19-9d43-2e812ba52663 · outbound

This paper cites North-Holland Publishing Company, 1976.

Toward Minimum Graphic Parity Networks North-Holland Publishing Company, 1976

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:42.136078Z

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Observation 35ee9d92-e954-475c-96e6-39f2f8c5b5a0 · outbound

This paper cites Error per single-qubit gate below 10−4 in a superconducting qubit.npj Quantum Information, 9(1):111, 2023.doi:10.1038/s41534-023-00781-x.

Toward Minimum Graphic Parity Networks Error per single-qubit gate below 10−4 in a superconducting qubit.npj Quantum Information, 9(1):111, 2023.doi:10.1038/s41534-023-00781-x

Reference 20

Resolution: verified exact; doi, observed 2026-08-04T18:28:49.332901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9dacbd2e-3d34-458a-9d1d-8899daac5403 · outbound

This paper cites Ising formulations of many NP problems.Frontiers in Physics, 2,.

Toward Minimum Graphic Parity Networks Ising formulations of many NP problems.Frontiers in Physics, 2,

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:42.446805Z

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Observation 4bc161c7-acd4-451d-9285-9a174026b8fe · outbound

This paper cites Depth optimization of cz, cnot, and clifford circuits.IEEE Transactions on Quantum Engineering, 3:1–8, 2022.doi:10.1109/TQE.2022.3180900.

Toward Minimum Graphic Parity Networks Depth optimization of cz, cnot, and clifford circuits.IEEE Transactions on Quantum Engineering, 3:1–8, 2022.doi:10.1109/TQE.2022.3180900

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:42.673258Z

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Observation 7883ae43-fd76-4dd5-8f87-7f5e6677514b · outbound

This paper cites Quan- tum Circuits for General Multiqubit Gates.Physical Review Letters, 93(13):130502, sep 2004.

Toward Minimum Graphic Parity Networks Quan- tum Circuits for General Multiqubit Gates.Physical Review Letters, 93(13):130502, sep 2004

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:42.779668Z

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Observation b8550b75-a290-42ed-b04b-d1d15c0c91c8 · outbound

This paper cites Ross, Yuan Su, Andrew M.

Toward Minimum Graphic Parity Networks Ross, Yuan Su, Andrew M

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:42.939186Z

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Observation 4d6a4ea0-ad47-497e-b0fb-ccad446747bf · outbound

This paper cites Beating the break-even point with a discrete-variable-encoded logical qubit.Nature, 616(7955):56–60, April 2023.doi:10.1038/s41586-023-05784-4.

Toward Minimum Graphic Parity Networks Beating the break-even point with a discrete-variable-encoded logical qubit.Nature, 616(7955):56–60, April 2023.doi:10.1038/s41586-023-05784-4

Reference 25

Resolution: verified exact; doi, observed 2026-08-04T18:28:49.234004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 036f6f18-c91e-4e8e-becb-bad86b55833e · outbound

This paper cites Total Ordering Problem.SIAM Journal on Computing, 8(1):111–114, 1979.doi:10.1137/0208008.

Toward Minimum Graphic Parity Networks Total Ordering Problem.SIAM Journal on Computing, 8(1):111–114, 1979.doi:10.1137/0208008

Reference 26

Resolution: verified exact; doi, observed 2026-08-04T18:28:49.168320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4e891e8b-d6ab-4586-be6c-abb18ca9eb90 · outbound

This paper cites Collins, Arinjoy De, Paul W.

Toward Minimum Graphic Parity Networks Collins, Arinjoy De, Paul W

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:43.396881Z

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Observation 9351b1a3-144c-4ca7-a803-9e238a1ceef0 · outbound

This paper cites an unresolved cited work.

Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:43.488577Z

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Observation 84af82c0-ba48-40e8-aeb1-6179573321ee · outbound

This paper cites Triangulated graphs and the elimination process.Journal of Mathematical Analysis and Applications, 32(3):597–609, December 1970.

Toward Minimum Graphic Parity Networks Triangulated graphs and the elimination process.Journal of Mathematical Analysis and Applications, 32(3):597–609, December 1970

Reference 29

Resolution: verified exact; doi, observed 2026-08-04T18:28:49.021153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 52638bcb-8444-4651-a0e7-c670d1801cd7 · outbound

This paper cites Dreiling, John P.

Toward Minimum Graphic Parity Networks Dreiling, John P

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:43.673714Z

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Observation 0ffeaaf0-da1f-48c8-8a22-a7a2bc030f7a · outbound

This paper cites an unresolved cited work.

Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:43.784017Z

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Observation fd496f59-d497-4245-800b-9c3dc2e9dc2d · outbound

This paper cites Efficient Decomposition of Quantum Gates.Physical Review Letters, 92(17):177902, 2004.

Toward Minimum Graphic Parity Networks Efficient Decomposition of Quantum Gates.Physical Review Letters, 92(17):177902, 2004

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:43.920924Z

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Observation 0149caf9-c786-46a1-934a-18d2e9f8f609 · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:44.043114Z

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Observation 95e0d1c2-4c2f-4a65-b1fe-cc3ebe72b41a · outbound

This paper cites Optimization of CNOT circuits on limited-connectivity architecture.Physical Review Re- search, 5(1):13065, 2023.

Toward Minimum Graphic Parity Networks Optimization of CNOT circuits on limited-connectivity architecture.Physical Review Re- search, 5(1):13065, 2023

Reference 34

Resolution: malformed identifier; no resolver link, observed 2026-08-04T18:23:44.175376Z

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Observation 409da1dd-f527-41ca-9e7d-489cf923b95d · outbound

This paper cites MaxCut quantum approximate optimization algorithm performance guarantees for p > 1.Physical Review A, 103(4):042612, April 2021.

Toward Minimum Graphic Parity Networks MaxCut quantum approximate optimization algorithm performance guarantees for p > 1.Physical Review A, 103(4):042612, April 2021

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:44.265066Z

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Observation 4b99b5c3-31ad-4dc6-adfb-7f68c0e71f5f · outbound

This paper cites Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs.Physical Review A, 104(5):052419, November 2021.doi:10.1103/PhysRevA.104.052419.

Toward Minimum Graphic Parity Networks Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs.Physical Review A, 104(5):052419, November 2021.doi:10.1103/PhysRevA.104.052419

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:44.398787Z

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Observation ce9ea5af-ca9a-4ce5-9b08-35b47a68b11b · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 37

Resolution: malformed identifier; no resolver link, observed 2026-08-04T18:23:44.586696Z

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Observation 09b73a22-1212-4a7d-b586-07a741f02050 · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:44.728817Z

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Observation 181aca5e-e296-46b2-9a70-030816ad3437 · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:44.876280Z

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Observation 1a571fd2-725d-4930-b904-0b719cc8f2cc · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:45.016157Z

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Observation 3a50e5c5-636f-4552-b6d3-f5500da2ad15 · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:45.137637Z

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Observation bbda5096-7aa3-44f8-9641-65962f767856 · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:45.263951Z

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Observation ca70153f-aae0-4126-ba4f-acdcaeebc016 · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:45.394223Z

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Observation 365fe046-afb2-47a2-bbd8-42f3a385d144 · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:45.565726Z

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Observation d7706534-38a2-44fb-b0ec-e7eb76fea21c · outbound

This paper cites In our algorithm, when working from the leaves to the root, we will keep track of all canonical representations of σ|N+σ (v) for v∈X t.

Toward Minimum Graphic Parity Networks In our algorithm, when working from the leaves to the root, we will keep track of all canonical representations of σ|N+σ (v) for v∈X t

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-04T18:23:45.666129Z

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Observation 6e3ce060-5c34-4c9b-88f2-f87e06432fca · outbound

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Toward Minimum Graphic Parity Networks Unresolved cited work

Reference 2014

Resolution: malformed identifier; no resolver link, observed 2026-08-04T18:23:42.555026Z

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Pith citing papers

Observation 4c0e4471-969b-4b22-99b9-ad501704e58e · inbound

CNOT-Distance is NP-complete under all-to-all connectivity cites this paper.

CNOT-Distance is NP-complete under all-to-all connectivity Toward Minimum Graphic Parity Networks

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:55:26.797730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.