Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition | Paper Citation Record

Observation 88cb698f-2681-42b3-adbc-14f9ae48badc · outbound

This paper cites ForA∈SL(2,F 3), define the graph plane Γ(A) :={(x,Ax) :x∈V A}⊂V A⊕VB.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition ForA∈SL(2,F 3), define the graph plane Γ(A) :={(x,Ax) :x∈V A}⊂V A⊕VB

Reference 1

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This paper cites an unresolved cited work.

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Reference 2

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Observation c6abc774-66b0-4eb4-9a97-22746f9a28cb · outbound

This paper cites Let Stab(Σ) :={M∈Sp(4,F 3) :M(Σ) = Σ} be its setwise stabilizer.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Let Stab(Σ) :={M∈Sp(4,F 3) :M(Σ) = Σ} be its setwise stabilizer

Reference 3

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Observation 2c7fd137-17b7-4ddf-9676-efb3a2f8be46 · outbound

This paper cites Let H0 loc := SL(VA)×SL(V B)⊂Sp(V) be the strict local symplectic subgroup preservingVA and VB separately.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Let H0 loc := SL(VA)×SL(V B)⊂Sp(V) be the strict local symplectic subgroup preservingVA and VB separately

Reference 4

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Reference 5

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Observation e7663e4e-1e8d-45d8-a32a-9a0b2e306ac6 · outbound

This paper cites For a two-qutrit Clifford coreK, writeS K :=π(K), and define Kgood :={K∈Cliff 2,3 :S K∈S good}.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition For a two-qutrit Clifford coreK, writeS K :=π(K), and define Kgood :={K∈Cliff 2,3 :S K∈S good}

Reference 6

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Observation e0a6fe79-d67c-4833-bdbf-6dbb2c816216 · outbound

This paper cites At the symplectic-label level, a direct finite-field computation gives a local reversing symmetry R∗∈Sp(V A)×Sp(V B) such that R∗SKClR−1 ∗ =S−1 KCl.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition At the symplectic-label level, a direct finite-field computation gives a local reversing symmetry R∗∈Sp(V A)×Sp(V B) such that R∗SKClR−1 ∗ =S−1 KCl

Reference 7

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Observation de8d9fde-00e8-454c-98ff-0fe7ccc53c44 · outbound

This paper cites IfK=K T , thenK † =K, and forX∈su(9) τ(AdKX) = (KXK−1)T = (KT )−1XTKT = AdK−1(τX).

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition IfK=K T , thenK † =K, and forX∈su(9) τ(AdKX) = (KXK−1)T = (KT )−1XTKT = AdK−1(τX)

Reference 8

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Observation 942d8061-10b3-4bdf-b7f8-99369b01d911 · outbound

This paper cites (11) and (12).

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition (11) and (12)

Reference 9

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Reference 10

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Observation d90ce3f5-b974-4d42-b529-78240c23b5fb · outbound

This paper cites One convention detail deserves an explicit statement.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition One convention detail deserves an explicit statement

Reference 11

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Observation a609d1f2-e2e1-4d88-a6c3-6212f2e4583b · outbound

This paper cites Each local layer is parameterized by a real 16-vector pi = (ai,bi)∈R 8⊕R 8 using the Gell–Mann basis: Li(pi) = exp i 8X α=1 ai,αλα ! ⊗exp i 8X α=1 bi,αλα !.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Each local layer is parameterized by a real 16-vector pi = (ai,bi)∈R 8⊕R 8 using the Gell–Mann basis: Li(pi) = exp i 8X α=1 ai,αλα ! ⊗exp i 8X α=1 bi,αλα !

Reference 12

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Observation 79fd5633-70f1-42fb-b817-a9d854f3d09d · outbound

This paper cites We test this condition with a one- dimensional finite-difference scan in validation-order lo- cal coordinates.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition We test this condition with a one- dimensional finite-difference scan in validation-order lo- cal coordinates

Reference 13

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Observation 3a51791e-0c6f-43f1-b7f6-b2438c0d97a3 · outbound

This paper cites It then searches for a second pointh (m) reg ∈L 5 satisfying Φval KCl(h(m) reg )≈U (m) bad and having full-rank differential.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition It then searches for a second pointh (m) reg ∈L 5 satisfying Φval KCl(h(m) reg )≈U (m) bad and having full-rank differential

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:35:51.185115Z

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Observation 11f82f21-97e9-4f6d-886c-2d7fc5527a33 · outbound

This paper cites The aggregate statistics are shown in Table III.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition The aggregate statistics are shown in Table III

Reference 15

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Observation d559495f-3c3e-432f-8db4-9ae7b058e356 · outbound

This paper cites The archive separates raw local-layer parameters, critical-candidate genera- tion records, strict verification outputs, aggregate sum- mary files, and figure-generation inputs.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition The archive separates raw local-layer parameters, critical-candidate genera- tion records, strict verification outputs, aggregate sum- mary files, and figure-generation inputs

Reference 16

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Observation 7fc7e672-0c74-4795-81b4-56519ee3bcb7 · outbound

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Reference 17

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Observation db85eb8e-2313-4d09-aa43-cef30c31e6c7 · outbound

This paper cites Barenco, C.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Barenco, C

Reference 18

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Reference 19

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Observation 9f2e9ebc-37f2-4db3-b8cc-5cd0fe24892e · outbound

This paper cites The Solovay-Kitaev algorithm.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition The Solovay-Kitaev algorithm

Reference 20

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Observation 392d3e25-8e8c-43be-844c-05ece2ae18e3 · outbound

This paper cites Khaneja, R.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Khaneja, R

Reference 21

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Observation d5a56ea2-1780-4d11-899b-34f41b0c47eb · outbound

This paper cites Makhlin, Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum compu- tations, Quantum Information Processing1, 243 (2002).

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Makhlin, Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum compu- tations, Quantum Information Processing1, 243 (2002)

Reference 22

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Observation b53a98b1-7b5a-4250-bd93-d28a06eeac7d · outbound

This paper cites Zhang, J.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Zhang, J

Reference 23

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Observation 6fa733f5-3648-4bae-aedd-ff670c744d02 · outbound

This paper cites Vidal and C.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Vidal and C

Reference 24

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Observation 83ca77e3-00a5-4670-9383-60df17663aab · outbound

This paper cites Vatan and C.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Vatan and C

Reference 25

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Observation 862766b3-b1db-419a-bbaa-6e54f65bcb95 · outbound

This paper cites M¨ ott¨ onen, J.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition M¨ ott¨ onen, J

Reference 26

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Reference 27

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Reference 28

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Observation e2a85382-c626-4245-8eb2-b7b8faaaf2b1 · outbound

This paper cites Universal quantum gates.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Universal quantum gates

Reference 29

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Observation 1f549d56-14b1-47f6-a20e-0ad80e65b8e9 · outbound

This paper cites Muthukrishnan and C.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Muthukrishnan and C

Reference 30

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Observation 41f837f4-632e-4278-90bc-d1f4bb485c3f · outbound

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Reference 31

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Observation 85c9e05f-0b54-49db-997d-2bcae59c6328 · outbound

This paper cites Efficient Circuits for Exact-Universal Computations with Qudits.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Efficient Circuits for Exact-Universal Computations with Qudits

Reference 32

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Observation 0b56e033-ffcc-4b09-8baa-1c7a57c9fbfd · outbound

This paper cites Di and H.-R.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Di and H.-R

Reference 33

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Reference 34

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Reference 35

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Reference 36

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Observation f23cd40d-a6b6-43e4-811a-0aebdabaf13b · outbound

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Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Unresolved cited work

Reference 37

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Observation be46b95b-9022-45e8-9933-3697b5877b68 · outbound

This paper cites Optimal synthesis of general multi-qutrit quantum computation.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Optimal synthesis of general multi-qutrit quantum computation

Reference 38

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Observation 18c98b25-9ce7-4a45-b971-21927ff2ebfc · outbound

This paper cites Krantz, M.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Krantz, M

Reference 39

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Observation a6e30996-fd86-4e2f-b27a-cc9c58fc544c · outbound

This paper cites Kjaergaard, M.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Kjaergaard, M

Reference 40

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Observation 7c67237d-dc57-4c95-b771-fe773fbce2db · outbound

This paper cites Blais, A.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Blais, A

Reference 41

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Reference 42

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Reference 43

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Reference 44

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Observation 9d0c83f6-ab14-481c-b19a-1821dbda0f05 · outbound

This paper cites Morvan, V.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Morvan, V

Reference 45

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Reference 46

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Reference 47

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Observation 8a4011c8-3440-4d1e-8867-aae9626a035a · outbound

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Reference 48

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Reference 49

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Observation 8143c06f-a38b-4601-9b82-ee15be5223c2 · outbound

This paper cites Subramanian and A.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Subramanian and A

Reference 50

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This paper cites Fault-Tolerant Quantum Computation with Higher-Dimensional Systems.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Fault-Tolerant Quantum Computation with Higher-Dimensional Systems

Reference 51

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Observation 3490313a-e789-4b41-99be-daeb6e222269 · outbound

This paper cites Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic

Reference 52

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Observation 2beba047-3175-40f8-b82d-0c4105c0db01 · outbound

This paper cites an unresolved cited work.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Unresolved cited work

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-15T15:35:50.522821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5413499-e7bc-4b7e-a983-3a2740228cc6 · outbound

This paper cites Lambert, E.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Lambert, E

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-15T15:35:50.526622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b932418-c8c0-4c8d-95fb-c28997f5477a · outbound

This paper cites an unresolved cited work.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:35:50.855036Z

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.

Observation d54b3f13-af16-46d8-a18e-4b2ea26671ae · outbound

This paper cites Hoffman and S.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Hoffman and S

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:35:50.843296Z

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.

Observation b00f14a5-6385-49d8-a03b-2b8bbf7b68e1 · outbound

This paper cites Guillemin and A.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Guillemin and A

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:35:50.830376Z

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.

Observation a59e2b8f-1e40-452f-aead-7080e83a5a9f · outbound

This paper cites Whitney, On singularities of mappings of euclidean spaces.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Whitney, On singularities of mappings of euclidean spaces

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:35:50.817721Z

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.

Observation c14365b1-c191-470f-803f-da074b87f160 · outbound

This paper cites Golubitsky and V.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Golubitsky and V

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:35:50.804966Z

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.

Observation 5a8673ea-fded-46eb-ae5c-d8bfc4a1bd1b · outbound

This paper cites On the Entangling Power of Quantum Evolutions.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition On the Entangling Power of Quantum Evolutions

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-15T15:35:50.548997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3015b2cf-237c-43ed-9cf0-8a0a29ca49f6 · outbound

This paper cites an unresolved cited work.

Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition Unresolved cited work

Reference 61

Resolution: verified exact; raw_fallback, observed 2026-08-15T15:35:50.647316Z

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.

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Reference resolution

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