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Paper Citation Record · LEDGER

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom

As of 15 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 6 inbound Pith citation observations for arXiv:2507.15056.

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

pith.paper-citation-record.v1
2507.15056 v1

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:54:37.319163Z

measured 57 of 57 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 6 of 6 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T08:00:03.979334Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-21T19:15:31.096658Z

Reference resolution

51 of 51 outbound references displayed

  • verified exact4
  • verified fuzzy23
  • unresolved24
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 033cfb44-d968-4370-8ca2-157b3ae6aa2b · outbound

This paper cites [2, 10, 37, 38] applicable to more general stabilizer codes including non-Pauli stabilizer models.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom [2, 10, 37, 38] applicable to more general stabilizer codes including non-Pauli stabilizer models

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:33.332527Z digest=sha256:f239e55f2d82ef41302f3af4ab26bb6d5262ea95abfdc6d9f343e4bb38c718d1

Observation 03d6a8e3-8f95-45a9-8f00-215eedda1b59 · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 2

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:34.013792Z digest=sha256:1abefb628cb33966584f7c0ead4cc1e268d231068341757528b51565e367018f

Observation 7ea5d9d6-b4b8-4bc2-8f99-1fd1fec7954d · outbound

This paper cites 4.sys q( fM;Z 2) =sys 2q( fM;Z 2) = Ω(N 2 3 ), sysq( fM;Z 2) =sys 2q( fM;Z 2) = Ω(N 2 3 ).

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom 4.sys q( fM;Z 2) =sys 2q( fM;Z 2) = Ω(N 2 3 ), sysq( fM;Z 2) =sys 2q( fM;Z 2) = Ω(N 2 3 )

Reference 3

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raw_fallback, observed 2026-08-06T15:54:38.471482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:33.802871Z digest=sha256:fc60a0e526c606d8943e82eec16ebcb00095e1aab0e220709c2d7185596a9c21

Observation deb2b39f-26ec-414d-9699-8012d68479cf · outbound

This paper cites 2.vol( fM) = Θ(N).

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom 2.vol( fM) = Θ(N)

Reference 4

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raw_fallback, observed 2026-08-06T15:54:38.479189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:33.692152Z digest=sha256:9f615868785bd1948e501d0d0e6192a4ae61e6bc25262aaffa798f2e87c27b8e

Observation 8e38e0a6-d440-4657-ac6c-bcbb55b22440 · outbound

This paper cites bad dimensions.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom bad dimensions

Reference 5

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raw_fallback, observed 2026-08-06T15:54:38.463681Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:33.910327Z digest=sha256:0f6086f9546fdbbbfde1501bcae5dc92812576383764a7434340050fb0469c85

Reference 6

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-06T15:54:34.296179Z digest=sha256:a71c51620cf73f760cb4b51cd5fe1faf82a971d360cebea3fb3a449ef3cf3fcb

Observation 67912735-9d6e-46de-b71d-c286b4afb226 · outbound

This paper cites Similarly,a ∗7 is the Poincar´ e dual cocycle of the cycle a4.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Similarly,a ∗7 is the Poincar´ e dual cocycle of the cycle a4

Reference 7

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:33.540449Z digest=sha256:9787b7121cb9ec2b08b44aa3ed0306e20fa4d184bffa8a17829621c40fe4d45d

Observation 644d9e0b-1b4b-42fc-be42-8fa5485125c3 · outbound

This paper cites Hastings, J.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Hastings, J

Reference 8

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raw_fallback, observed 2026-08-06T15:54:38.456070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:33.956722Z digest=sha256:1aa62e11bda591050ea93d9680b0661be3a6022fdf011d05a92c7919391820ad

Observation e1c72e3e-b9ca-4f55-b1d0-5fcce0400bbc · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 9

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:34.055168Z digest=sha256:0a991a7540186ad5e9248577f12afeef1c28938109a3ddca50d5f25a0984c97e

Observation 8603aa27-7c9a-4ac5-a505-fc46a8ccfb9d · outbound

This paper cites Gromov, Systoles and intersystolic inequalities, Actes de la Table Ronde de G´ eom´ etrie Diff´ erentielle (Luminy, 1992), 291—362, S´ emin.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Gromov, Systoles and intersystolic inequalities, Actes de la Table Ronde de G´ eom´ etrie Diff´ erentielle (Luminy, 1992), 291—362, S´ emin

Reference 10

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raw_fallback, observed 2026-08-06T15:54:38.438934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:34.169782Z digest=sha256:f20b955a2c007f8975f3eca4415af15fb32702ffbc364b0023e7d82179b54b9e

Observation 4056bca9-48ba-4f9b-8149-ad9cdb088104 · outbound

This paper cites Panteleev and G.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Panteleev and G

Reference 11

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verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.429826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:34.220534Z digest=sha256:5cab83fdc979dd4c44e380c455236a337a3ce2f5749e120a853c48f5f507f0eb

Observation bc8bf259-9373-4a1d-b1aa-0a2b7f2d00a3 · outbound

This paper cites Cross, Z.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Cross, Z

Reference 12

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no resolver link, observed 2026-08-06T15:54:34.749023Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:34.749023Z digest=sha256:3f42294dd9393a8943cdb9cf612657388ce026b3f5a0a1d4acbe7458d2ad3a59

Observation dcb20a9d-dd62-492d-b443-a8143a41d17b · outbound

This paper cites Panteleev and G.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Panteleev and G

Reference 13

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verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.421141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:34.344912Z digest=sha256:eecc3fddad2099fc381e32c007b95e1e31dca99a6d5572f8eedc1bd1b4305261

Observation 6b4e7567-ddba-436a-bdff-c2c961c3c4c9 · outbound

This paper cites Cohen, I.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Cohen, I

Reference 14

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raw_fallback, observed 2026-08-06T15:54:38.412926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:34.444931Z digest=sha256:4f9bdc0b45d519a51033708572dfa5766d6137a977215fe7e0da9fe9afee6120

Observation 4d446ca3-47b0-4736-98cb-f24f42bbf439 · outbound

This paper cites Huang, T.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Huang, T

Reference 15

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raw_fallback, observed 2026-08-06T15:54:38.404632Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:34.502795Z digest=sha256:e3ac41b1cef9b7d0626414778ac2f8681d21f52048729c933d79d04003c42592

Observation 905a8790-9968-4236-a337-19d5027d519c · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 16

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no resolver link, observed 2026-08-06T15:54:34.600317Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:34.600317Z digest=sha256:b413195b05249c99fb69063c719060fc369fb342d9cfe5dc919930ecf2ef6365

Observation 1a0a771e-6c9e-4fa5-83d6-35fb4421057d · outbound

This paper cites Fast and Parallelizable Logical Computation with Homological Product Codes.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Fast and Parallelizable Logical Computation with Homological Product Codes

Reference 17

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no resolver link, observed 2026-08-06T15:54:34.664293Z

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source=pdf_text observed=2026-08-06T15:54:34.664293Z digest=sha256:cc4a4cb0cc7f77eabe0a4c5bcb5885ff4cecc212cd8357a163a00d0a0abcd7ca

Observation 480d4a13-7ca2-444d-a5a0-aa8eccbe4a85 · outbound

This paper cites Kubica, B.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Kubica, B

Reference 18

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unresolved
no resolver link, observed 2026-08-06T15:54:35.257076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:35.257076Z digest=sha256:7cacb979f4b2ce7ef82cfb4ff6883eb7faf0b5cc9416a68a7be61ba79a0490fd

Observation 91e4c2ad-c69c-4032-be20-dabddff874dc · outbound

This paper cites Low-overhead fault-tolerant quantum computation by gauging logical operators.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Low-overhead fault-tolerant quantum computation by gauging logical operators

Reference 19

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no resolver link, observed 2026-08-06T15:54:34.825771Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:34.825771Z digest=sha256:4bd8887b6c9e372127f49f14eace07a40d42cee7be4dda643d6ccd18ae98a7db

Observation 1d89d1b9-1a54-402c-8237-1b1b7aa8aa2c · outbound

This paper cites For instance, in a 3D torus (with zero curvature), the distance is determined by the minimal length of the logical string operator, which scales asO(N 1 3 ).

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom For instance, in a 3D torus (with zero curvature), the distance is determined by the minimal length of the logical string operator, which scales asO(N 1 3 )

Reference 20

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raw_fallback, observed 2026-08-06T15:54:38.505082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:33.114826Z digest=sha256:2db285c24d967c1ed10d84ff2b251462e86a6a8c8aafc0e044c09cacbf0f5654

Observation b6f65314-b892-462f-aa8f-c37e596bd187 · outbound

This paper cites Swaroop, T.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Swaroop, T

Reference 21

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no resolver link, observed 2026-08-06T15:54:34.928906Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:34.928906Z digest=sha256:2fe01e324dd1996dac81179eb58ab987c60cff677286fcd10a039e7d4068b2fe

Observation 30b4106d-82f1-41c5-8f99-2613455c9ff3 · outbound

This paper cites Quantum LDPC Codes with Transversal Non-Clifford Gates via Products of Algebraic Codes.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Quantum LDPC Codes with Transversal Non-Clifford Gates via Products of Algebraic Codes

Reference 22

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no resolver link, observed 2026-08-06T15:54:34.983401Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:34.983401Z digest=sha256:2334c1142a886367cfadf5bf82baf8ae26a0bb9b4d343167dfd55cf682ec14a1

Observation 6f1df18d-5fd1-4696-95a2-c7e69afa62b6 · outbound

This paper cites Transversal non-Clifford gates for quantum LDPC codes on sheaves.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Transversal non-Clifford gates for quantum LDPC codes on sheaves

Reference 23

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no resolver link, observed 2026-08-06T15:54:35.090547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:35.090547Z digest=sha256:85ecb81aede6690bfe3b2c5519c2ef0bca51dc3a918f13320bb127f71a65d4bf

Observation e27a6d68-d0b6-4acd-9b04-cadd84d70b79 · outbound

This paper cites Bombin, Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes, New Journal of Physics17, 083002 (2015).

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Bombin, Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes, New Journal of Physics17, 083002 (2015)

Reference 24

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.177629Z digest=sha256:67412c1087607aac21f16ddf132af8936ef02ba77e7e872cbc7a171cc80e1899

Observation 2d06e8e1-cc08-49fd-9b29-fc667d127148 · outbound

This paper cites Vasmer and D.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Vasmer and D

Reference 25

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unresolved
no resolver link, observed 2026-08-06T15:54:35.372776Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:35.372776Z digest=sha256:6bab0d618437b842cf7db0a1ec67c194fffbeaf6e9e959d056a20ae9d7c6081d

Observation 6e890265-1b0c-40cc-a56a-d6905da81195 · outbound

This paper cites Bravyi and R.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Bravyi and R

Reference 26

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verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.378408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.452114Z digest=sha256:a446a73b3f8c3b37b5ce7388c418f6fd24626c289f9da59a0cb529c74cf683d8

Reference 27

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no resolver link, observed 2026-08-06T15:54:35.544276Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:35.544276Z digest=sha256:e40701a267dd56534e8712c4698d44a77226251a2111e8f1a9415f8d45f4a80f

Observation 0a660acc-639f-4045-bdd2-ed8ebcfaa3c2 · outbound

This paper cites Barkeshli, Y.-A.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Barkeshli, Y.-A

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.370341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.600769Z digest=sha256:1e26859a65b6f9f9112567bbaeb3ab13f8089581e5001c5a6d9a7e642f010978

Observation 68aace2e-e2ef-46c2-b336-0692768d7c7c · outbound

This paper cites Barkeshli, Y.-A.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Barkeshli, Y.-A

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.361764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.705330Z digest=sha256:15a9beaa0e31a6b3a8ca216ae7292fc80e8c9767d1c0d03327aa5e115d253642

Observation e32f8c7e-87a2-4556-8751-149f8d78f1ae · outbound

This paper cites Yoshida, Topological color code and symmetry- 18 protected topological phases, Phys.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Yoshida, Topological color code and symmetry- 18 protected topological phases, Phys

Reference 30

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verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.353508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.774641Z digest=sha256:3c8648309fc5e6edb8febc64b5eede3a233b82ac84fbd1c66d673d2abbce1513

Observation 0e6d0141-393b-4e08-b138-d8a568929cf6 · outbound

This paper cites Yoshida, Topological phases with generalized global symmetries, Phys.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Yoshida, Topological phases with generalized global symmetries, Phys

Reference 31

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no resolver link, observed 2026-08-06T15:54:35.853000Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:35.853000Z digest=sha256:a23810976589e8593c93ba81d184fb8185e22aa51c50c3c0aacd81a4f6645b13

Observation 28b51524-b350-48d1-8c19-d52b679bbed8 · outbound

This paper cites Yoshida, Gapped boundaries, group cohomology and fault-tolerant logical gates, Annals of Physics377, 387 (2017).

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Yoshida, Gapped boundaries, group cohomology and fault-tolerant logical gates, Annals of Physics377, 387 (2017)

Reference 32

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raw_fallback, observed 2026-08-06T15:54:38.337427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.941294Z digest=sha256:ba6540fe5a8d05a9a24fbef2ec0d3ac25eca76d4b5babacfb1f4d8a545011982

Observation de42d2a8-9b6f-456b-98ea-34e4573463da · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-06T15:54:38.327839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.977088Z digest=sha256:7aa44585b5d172af157ae9f1c26bee54ec36bf97a1997f2fb37b563233cfa056

Observation 0a37fe9b-4151-423e-ab68-2fac9b49c88f · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-06T15:54:38.319806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:35.993108Z digest=sha256:61d28f0c1d835c5d6daa9dc638696903f7b4a14e44673e1147039dda96604280

Observation 3e9a7fd1-c4a2-4ce2-938a-c82f5f938d4b · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:36.144494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:36.144494Z digest=sha256:aeebedf75e06c28677e611a2597a8f327eb4ed486f32c9e736df3e5ea98f2a35

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:36.194019Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:36.194019Z digest=sha256:e39295d55808d032b30db0ebac2fd299f5f46be81aecc4a071e5fe1f8ee56698

Observation bf9b4440-fd88-428a-82b0-c2acd720485c · outbound

This paper cites Cups and Gates I: Cohomology invariants and logical quantum operations.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Cups and Gates I: Cohomology invariants and logical quantum operations

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:36.354896Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:36.354896Z digest=sha256:56fb0dd255048e767da30c3ccb1495ba904bc960bf4bd77dc0da6cb5c4e097a3

Observation d0c2db4a-52e2-4db4-a4f7-b44d180ae91d · outbound

This paper cites McCullough and H.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom McCullough and H

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.311426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:36.492775Z digest=sha256:38720936953d1ee2e47b1fc2e2ae178c82e568f519bdd784bcf85a7eeb0d5cfb

Observation 2a3db7cc-9f8e-4383-ae62-895a49faa7b9 · outbound

This paper cites Dotterrer, L.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Dotterrer, L

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.303292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:36.548262Z digest=sha256:e421b3b4fad6a59ba49ba0e274335186360cf907529ec78dc92c60431fc9a117

Observation 18119b30-61d1-4bba-99d3-603f66bd1dab · outbound

This paper cites Collapsibility and vanishing of top homology in random simplicial complexes.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Collapsibility and vanishing of top homology in random simplicial complexes

Reference 40

Resolution
verified exact
local_arxiv, observed 2026-08-06T15:54:37.589091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:36.702007Z digest=sha256:f647e6fe7cc058b9b675ea79da0ba63762b5bd6e6359d24005c4dc7efd1891a9

Observation cb61c6f9-a950-4353-a332-4e8e46fd4d7c · outbound

This paper cites Linial* and R.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Linial* and R

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.295106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:36.799650Z digest=sha256:ac7a8237937c1b9b3f63404f690dd8b4a40152cb936df36e91b660501d3653ba

Observation c95ced72-033b-4bf2-8437-247a6485dc20 · outbound

This paper cites Homological connectivity of random k-dimensional complexes.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Homological connectivity of random k-dimensional complexes

Reference 42

Resolution
verified exact
local_arxiv, observed 2026-08-06T15:54:37.465438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:36.835354Z digest=sha256:73cca035603866a6c12c26e92204c26a43677a58f89a572a6fcf75a9fea1d545

Observation dbe79c05-2800-433a-a048-672ab475e27f · outbound

This paper cites Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:36.901487Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:36.901487Z digest=sha256:53793f017bbe8292ee4f4ecc2b867801dced994eb07330a9ba17896815bc3ce9

Observation 056d673d-4bcf-42da-a9b0-eb27b7ef93cb · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 44

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:37.000343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:37.000343Z digest=sha256:0b3196629465976917c51ca4fb428266c1c2ea0ed210aed778f472a345d53b4c

Observation deffe971-358b-400a-9134-58e7c2537cb1 · outbound

This paper cites an unresolved cited work.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Unresolved cited work

Reference 45

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:37.002852Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:37.002852Z digest=sha256:a9824a9295608459150bdbdeb521964287bbb915965b241939930942dc938584

Observation d2dd84b8-501e-4e74-874e-7bbd7d33f1f2 · outbound

This paper cites Local Quantum Codes from Subdivided Manifolds.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Local Quantum Codes from Subdivided Manifolds

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:37.005387Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:37.005387Z digest=sha256:e1628fc5b3343dd0783dbcc021f65345d3c467a75093dc1ba662c606c96e983a

Observation fbb85d87-cc17-4234-975c-c1a66180e209 · outbound

This paper cites Bacon, Operator quantum error-correcting subsys- tems for self-correcting quantum memories, Physical Re- view A73, 012340 (2006).

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Bacon, Operator quantum error-correcting subsys- tems for self-correcting quantum memories, Physical Re- view A73, 012340 (2006)

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.282209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:37.060958Z digest=sha256:6608c592b1e5bf26aabd59958b4ab54d679221e7b75caf623836f1a409b52d95

Observation 06cbd419-0aac-47f3-9dd2-28e5413b21a5 · outbound

This paper cites Hatcher, Algebraic Topology (CUP, Cambridge; New York, 2001).

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Hatcher, Algebraic Topology (CUP, Cambridge; New York, 2001)

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T15:54:38.272796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:37.140273Z digest=sha256:8f8a83db7357b0f078aebac9e53f3d861c418683c93c671a765eddf31e331be1

Observation 5f07ce7d-1714-46d8-ac14-4b12e59c31be · outbound

This paper cites Volume of Riemannian manifolds, geometric inequalities, and homotopy theory.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Volume of Riemannian manifolds, geometric inequalities, and homotopy theory

Reference 49

Resolution
verified exact
local_arxiv, observed 2026-08-06T15:54:37.773445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:37.206144Z digest=sha256:dd2ddd5accb70b47a75db9e4725b1bfffe9a1f36738d3ddf21ec64efba70dc22

Observation 5e18b50a-2d68-479a-9a5e-0255348eeaab · outbound

This paper cites Lifting a CSS code via its handlebody realization.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Lifting a CSS code via its handlebody realization

Reference 50

Resolution
verified exact
local_arxiv, observed 2026-08-06T15:54:37.762381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T15:54:37.260299Z digest=sha256:ddc6d91385d63154b210e45aec6c02d693d2771624b9cf1d0d9456a1cbe28d45

Observation d6c6f646-f5ac-4658-b07b-eb3bffed68de · outbound

This paper cites Bravyi, A.

Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Bravyi, A

Reference 51

Resolution
unresolved
no resolver link, observed 2026-08-06T15:54:37.319163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T15:54:37.319163Z digest=sha256:e3fc0928798574308fd82c3e8b169063d653674f6f4704a3adf1197d1fd13e9f

Pith citing papers

Observation 7dbaf634-9ca4-4329-8f82-4f30a3918afa · inbound

Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes cites this paper.

Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom

Reference 101

Resolution
verified exact
arxiv_id, observed 2026-05-18T22:51:52.931375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-18T22:51:30.133403Z digest=sha256:58846065552784226e6431e797301f06a7b4364763bf0a384155815429064e59

Observation a1c58749-90d6-4cd2-a79e-0827669f1303 · inbound

Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic cites this paper.

Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom

Reference 24

Resolution
verified exact
arxiv_id, observed 2026-05-21T19:15:31.099017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-21T19:14:49.965519Z digest=sha256:39e11bdc73d116c92557e8e42fc754b02ae29567de7c5e145aeb3b15616e4988

Observation df9a1729-9b78-46a6-abcb-0f525b079543 · inbound

Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates cites this paper.

Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom

Reference 19

Resolution
verified exact
arxiv_id, observed 2026-05-17T20:20:11.704107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-17T20:18:27.901205Z digest=sha256:c6a97a06735345c561bf25106ca639864601247d1a41ddbe9ea192d87eb87e25

Observation c77d531f-889f-4853-82dd-e3c457a5a776 · inbound

Multivariate Multicycle Codes for Complete Single-Shot Decoding cites this paper.

Multivariate Multicycle Codes for Complete Single-Shot Decoding Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom

Reference 124

Resolution
unresolved
no resolver link, observed 2026-08-03T08:00:03.979334Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-03T08:00:03.979334Z digest=sha256:b6bb389cee47cf4716929b7464045485020f567e7b602aa1a302d690310e2a77

Observation 5baca1e6-7945-4576-bf74-2dcfbd534be2 · inbound

Achieving Optimal-Distance Atom-Loss Correction via Pauli Envelope cites this paper.

Achieving Optimal-Distance Atom-Loss Correction via Pauli Envelope Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom

Reference 56

Resolution
verified exact
arxiv_id, observed 2026-05-15T17:06:19.174221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-05-15T17:03:21.262684Z digest=sha256:0298ef6e4232f72b74cdfd639a233c736a559e008ac30492ead53b9378396fd2

Observation a859f022-84c6-4964-b79f-2cc15f5702e1 · inbound

Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes cites this paper.

Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom

Reference 39

Resolution
unresolved
no resolver link, observed 2026-07-13T14:10:32.422124Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-13T14:10:32.422124Z digest=sha256:2c236c7456c6a42ceb0ce4df164db992d2e8e5d0e0febdf16c9fed99094562d6