Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T15:54:37.319163Z
Paper Citation Record · LEDGER
As of 8 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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T15:54:37.319163Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-03T08:00:03.979334Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-21T19:15:31.096658Z
51 of 51 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 033cfb44-d968-4370-8ca2-157b3ae6aa2b · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 03d6a8e3-8f95-45a9-8f00-215eedda1b59 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7ea5d9d6-b4b8-4bc2-8f99-1fd1fec7954d · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation deb2b39f-26ec-414d-9699-8012d68479cf · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8e38e0a6-d440-4657-ac6c-bcbb55b22440 · outbound
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 25f665f5-73e2-4a01-bc72-cf6f9d78d02d · outbound
Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Balanced Product Quantum Codes
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 67912735-9d6e-46de-b71d-c286b4afb226 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 644d9e0b-1b4b-42fc-be42-8fa5485125c3 · outbound
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e1c72e3e-b9ca-4f55-b1d0-5fcce0400bbc · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8603aa27-7c9a-4ac5-a505-fc46a8ccfb9d · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4056bca9-48ba-4f9b-8149-ad9cdb088104 · outbound
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bc8bf259-9373-4a1d-b1aa-0a2b7f2d00a3 · outbound
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation dcb20a9d-dd62-492d-b443-a8143a41d17b · outbound
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6b4e7567-ddba-436a-bdff-c2c961c3c4c9 · outbound
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4d446ca3-47b0-4736-98cb-f24f42bbf439 · outbound
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 905a8790-9968-4236-a337-19d5027d519c · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1a0a771e-6c9e-4fa5-83d6-35fb4421057d · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 480d4a13-7ca2-444d-a5a0-aa8eccbe4a85 · outbound
Reference 18
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 91e4c2ad-c69c-4032-be20-dabddff874dc · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1d89d1b9-1a54-402c-8237-1b1b7aa8aa2c · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b6f65314-b892-462f-aa8f-c37e596bd187 · outbound
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 30b4106d-82f1-41c5-8f99-2613455c9ff3 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6f1df18d-5fd1-4696-95a2-c7e69afa62b6 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e27a6d68-d0b6-4acd-9b04-cadd84d70b79 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2d06e8e1-cc08-49fd-9b29-fc667d127148 · outbound
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6e890265-1b0c-40cc-a56a-d6905da81195 · outbound
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a2043088-5cef-4f9c-a5ee-5e55c507c56a · outbound
Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Building manifolds from quantum codes
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0a660acc-639f-4045-bdd2-ed8ebcfaa3c2 · outbound
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 68aace2e-e2ef-46c2-b336-0692768d7c7c · outbound
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e32f8c7e-87a2-4556-8751-149f8d78f1ae · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0e6d0141-393b-4e08-b138-d8a568929cf6 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 28b51524-b350-48d1-8c19-d52b679bbed8 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation de42d2a8-9b6f-456b-98ea-34e4573463da · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0a37fe9b-4151-423e-ab68-2fac9b49c88f · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3e9a7fd1-c4a2-4ce2-938a-c82f5f938d4b · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f7ef84e7-1d7f-49e2-a35d-e6df6f1abd97 · outbound
Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom Graph codes and local systems
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bf9b4440-fd88-428a-82b0-c2acd720485c · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d0c2db4a-52e2-4db4-a4f7-b44d180ae91d · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2a3db7cc-9f8e-4383-ae62-895a49faa7b9 · outbound
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 18119b30-61d1-4bba-99d3-603f66bd1dab · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation cb61c6f9-a950-4353-a332-4e8e46fd4d7c · outbound
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c95ced72-033b-4bf2-8437-247a6485dc20 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation dbe79c05-2800-433a-a048-672ab475e27f · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 056d673d-4bcf-42da-a9b0-eb27b7ef93cb · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation deffe971-358b-400a-9134-58e7c2537cb1 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d2dd84b8-501e-4e74-874e-7bbd7d33f1f2 · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fbb85d87-cc17-4234-975c-c1a66180e209 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 06cbd419-0aac-47f3-9dd2-28e5413b21a5 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5f07ce7d-1714-46d8-ac14-4b12e59c31be · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5e18b50a-2d68-479a-9a5e-0255348eeaab · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d6c6f646-f5ac-4658-b07b-eb3bffed68de · outbound
Reference 51
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7dbaf634-9ca4-4329-8f82-4f30a3918afa · inbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a1c58749-90d6-4cd2-a79e-0827669f1303 · inbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation df9a1729-9b78-46a6-abcb-0f525b079543 · inbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c77d531f-889f-4853-82dd-e3c457a5a776 · inbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5baca1e6-7945-4576-bf74-2dcfbd534be2 · inbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a859f022-84c6-4964-b79f-2cc15f5702e1 · inbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.