Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T19:43:46.990545Z
Paper Citation Record · LEDGER
As of 15 August 2026, this Paper Citation Record lists 80 of 80 outbound references and 5 inbound Pith citation observations for arXiv:2506.16005.
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 2026-08-15T19:43:46.990545Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-14T05:14:10.183086Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z
80 of 80 outbound references displayed
External citation measurements
0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z
Observation 1200aeb7-72cb-40a9-91e5-ce69778cbbaf · outbound
No-go theorems for sublinear-depth group designs We show in Appendix A that a matchgate-invariant state ex- ists fork= 2
Reference 1
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 8b160d99-cc60-4bea-a548-484b0bbf8529 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 2
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 18d9cde6-4b15-49c9-b1d2-f7ada710a832 · outbound
No-go theorems for sublinear-depth group designs Here, the state (1⊗Ω|Φ⟩), where|Φ⟩is the Bell state, is aG-invariant state inH⊗2
Reference 3
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 fffb13c4-407d-46e6-a530-45171a4d6218 · outbound
No-go theorems for sublinear-depth group designs This is our first example of a group for which there is no invariant state atk= 2, ruling out the application of Theorem 1
Reference 4
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 f3d8809e-2f0a-4421-88b1-5f7c3a1c04a2 · outbound
No-go theorems for sublinear-depth group designs Here for the first time we have an invariant state atk= 1
Reference 5
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 eab2ed13-3263-4e98-b6b0-f412d1c39de4 · outbound
No-go theorems for sublinear-depth group designs non-local matchgate cir- cuits
Reference 6
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 c062fc48-525d-4c8a-8f0e-0d02ee1ce0ed · outbound
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 16075740-d480-4aca-ac8d-7b9c5e41e881 · outbound
Reference 8
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Unavailable: canonical work link unavailable.
Observation 7f7a6d18-fb2a-4057-9cc1-e69f83f045c4 · outbound
Reference 9
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Unavailable: canonical work link unavailable.
Observation 3f7455e6-6f79-4e58-abb8-6d2b175cd2d1 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 10
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Unavailable: canonical work link unavailable.
Observation 693e74ef-d03c-4e0d-bef6-75e1ffc38c64 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 11
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Unavailable: canonical work link unavailable.
Observation 11ff9c3a-097c-4b53-b444-59033995a7e2 · outbound
No-go theorems for sublinear-depth group designs Real classical shadows
Reference 12
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Unavailable: canonical work link unavailable.
Observation 46f6096f-db2b-494d-a3e2-13dc017b55ef · outbound
Reference 13
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 697fd111-c22d-48c5-bf64-d8e2049b02f2 · outbound
No-go theorems for sublinear-depth group designs Triply efficient shadow tomography
Reference 14
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Unavailable: canonical work link unavailable.
Observation fbb9a8ac-d89c-4385-926f-82c6ec6ebc29 · outbound
No-go theorems for sublinear-depth group designs Hardware-efficient learning of quantum many-body states
Reference 15
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Unavailable: canonical work link unavailable.
Observation ce4039a7-129f-4210-95d4-dee337bc9b88 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 16
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 0f918fd5-c5e2-4a9c-aaf5-3de7d721babf · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 17
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6da5f5a6-9597-4d5c-95c2-e501633c1170 · outbound
Reference 18
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Unavailable: canonical work link unavailable.
Observation 20222081-d753-4c6d-a7fa-493538949ac8 · outbound
No-go theorems for sublinear-depth group designs Hayden and J
Reference 19
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 aed705ba-3f54-4887-a894-1581465062ae · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 20
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 76a445b9-7866-4462-afb0-c217cfe3ddbb · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 21
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Unavailable: canonical work link unavailable.
Observation bb9c36e9-16e2-4ffa-b0ba-57699bae6228 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 22
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 93e793b8-1c53-4fe6-8ad3-f6568ab3da2f · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 23
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 9bdf64ff-6678-49fa-9fe0-a88595a015fc · outbound
No-go theorems for sublinear-depth group designs Unitary designs from statistical mechanics in random quantum circuits
Reference 24
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Unavailable: canonical work link unavailable.
Observation 0f3b7ba1-1c51-4a06-9377-1eeafe1c46f5 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 25
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 ba440950-928c-45bd-af0f-49360841317e · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 26
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Unavailable: canonical work link unavailable.
Observation 54682a51-6455-4228-bd6d-41a550d9945f · outbound
No-go theorems for sublinear-depth group designs Efficient Unitary T-designs from Random Sums
Reference 27
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Unavailable: canonical work link unavailable.
Observation 1ad538b9-3d09-49ef-b65a-460886a7147d · outbound
No-go theorems for sublinear-depth group designs Simple constructions of linear-depth t-designs and pseudorandom unitaries
Reference 28
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Unavailable: canonical work link unavailable.
Observation 3249078a-0ea8-4892-89c4-9b9b1c78bab5 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 29
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Unavailable: canonical work link unavailable.
Observation 71546205-6aac-4c7d-a986-dbf2442d5956 · outbound
No-go theorems for sublinear-depth group designs Incompressibility and spectral gaps of random circuits
Reference 30
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Unavailable: canonical work link unavailable.
Observation 5be63a85-db29-43e4-82cc-4f584356a328 · outbound
No-go theorems for sublinear-depth group designs Random unitaries in extremely low depth
Reference 31
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Unavailable: canonical work link unavailable.
Observation 9afe2db5-899e-4b81-871c-0ba814e0c018 · outbound
No-go theorems for sublinear-depth group designs Classical shadows of fermions with particle number symmetry
Reference 32
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Unavailable: canonical work link unavailable.
Observation 2fe72136-05c7-45c9-8220-c63e13b53564 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 33
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Unavailable: canonical work link unavailable.
Observation 65429f81-86a7-4893-8c6a-2e7bbdbe2d5d · outbound
Reference 34
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Unavailable: canonical work link unavailable.
Observation f0e0ca06-3267-499e-a032-73cb269ca48e · outbound
No-go theorems for sublinear-depth group designs Hashagen, S
Reference 35
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Unavailable: canonical work link unavailable.
Observation ecff1d43-754e-44e8-a6fb-12f3fca181cd · outbound
No-go theorems for sublinear-depth group designs Marvian, Restrictions on realizable unitary operations imposed by symmetry and locality, Nature Physics18, 283 (2022)
Reference 36
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Unavailable: canonical work link unavailable.
Observation 8fdb48da-c092-4c69-b8ec-6a30408ab02e · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 37
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 7e627584-8d16-4c99-a946-f005a7c61346 · outbound
No-go theorems for sublinear-depth group designs Fermionic Linear Optics and Matchgates
Reference 38
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Unavailable: canonical work link unavailable.
Observation 52c2a24f-6c60-463c-86c6-b8788bb6845a · outbound
No-go theorems for sublinear-depth group designs Jozsa and A
Reference 39
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Unavailable: canonical work link unavailable.
Observation d56e1c4d-a9a8-4e03-b22d-ca32ce596111 · outbound
No-go theorems for sublinear-depth group designs A complete theory of the Clifford commutant
Reference 40
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Unavailable: canonical work link unavailable.
Observation 3b8f99f1-ceeb-48f3-8421-2631d0744a84 · outbound
No-go theorems for sublinear-depth group designs García-Martín, P
Reference 41
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 a2dd37a6-4830-4974-b8c9-a99cf14631fc · outbound
No-go theorems for sublinear-depth group designs Linear programming with unitary-equivariant constraints
Reference 42
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Unavailable: canonical work link unavailable.
Observation be9051af-c6e9-49b3-b792-d2dd88b32239 · outbound
No-go theorems for sublinear-depth group designs Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information
Reference 43
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Unavailable: canonical work link unavailable.
Observation bdfe7fb6-d9f7-4481-9578-0be8a6d05f18 · outbound
No-go theorems for sublinear-depth group designs The mixed Schur transform: efficient quantum circuit and applications
Reference 44
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Unavailable: canonical work link unavailable.
Observation 2ecbab76-67ea-4412-ad87-5d695d2b34d6 · outbound
No-go theorems for sublinear-depth group designs Optimal Haar random fermionic linear optics circuits
Reference 45
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Unavailable: canonical work link unavailable.
Observation 776b209e-260a-42fc-932b-22d0166fa779 · outbound
No-go theorems for sublinear-depth group designs Unified Framework for Matchgate Classical Shadows
Reference 46
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Unavailable: canonical work link unavailable.
Observation 9ea6f809-5b2c-49b7-bfaf-3591dd8b9a0f · outbound
No-go theorems for sublinear-depth group designs Random ensembles of symplectic and unitary states are indistinguishable
Reference 47
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Unavailable: canonical work link unavailable.
Observation 85cb85e4-3423-4e6c-a7d5-82d614f3c69a · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 48
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Unavailable: canonical work link unavailable.
Observation 53280d4b-7749-49d1-abb8-bde2df65a5cd · outbound
No-go theorems for sublinear-depth group designs Benenti and G
Reference 49
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 5007349a-9657-41dd-83b4-bec81b85a088 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 50
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 0f7aaaeb-b937-49df-8ac9-0a59cd87b37f · outbound
No-go theorems for sublinear-depth group designs Showcasing a Barren Plateau Theory Beyond the Dynamical Lie Algebra
Reference 51
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 32bc8409-10f2-49b5-abaa-5a5b54af37fe · outbound
No-go theorems for sublinear-depth group designs The Clifford group fails gracefully to be a unitary 4-design
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 84294456-2943-4edd-b025-a672cf5d6956 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 53
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 d9e2206e-6ce1-4ff8-8397-c003091d705c · outbound
No-go theorems for sublinear-depth group designs Exponential learning advantages with conjugate states and minimal quantum memory
Reference 54
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 5484768d-9c8c-46bf-a032-4a983d67f399 · outbound
No-go theorems for sublinear-depth group designs Haah, Short remarks on shallow unitary circuits, arXiv preprint arXiv:2504.14005 (2025)
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 822db843-337e-433a-ab37-6f1c879bc5f6 · outbound
No-go theorems for sublinear-depth group designs Webb, The clifford group forms a unitary 3-design, Quantum Information and Computation16, 1379 (2016)
Reference 56
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation de06e833-2fe7-4a89-96c4-30a5fea4afa9 · outbound
Reference 57
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 90763d8b-c862-4d24-9918-dfac2d3da14f · outbound
No-go theorems for sublinear-depth group designs Real randomized measurements for analyzing properties of quantum states
Reference 58
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Unavailable: canonical work link unavailable.
Observation e50c549e-2d5c-4825-b69b-726e7fa260ac · outbound
Reference 59
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 6f65bafa-a00b-4778-b97f-278fa0138f8a · outbound
No-go theorems for sublinear-depth group designs A Survey of Quantum Property Testing
Reference 60
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Unavailable: canonical work link unavailable.
Observation fc36dc6e-e421-4933-8b0b-6d84aee1746f · outbound
No-go theorems for sublinear-depth group designs Fulton and J
Reference 61
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Unavailable: canonical work link unavailable.
Observation 0b33ca96-fc38-4478-9222-5bf92831b468 · outbound
No-go theorems for sublinear-depth group designs Wiersema, E
Reference 62
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f197096e-0146-4aaa-9305-557645a581a1 · outbound
No-go theorems for sublinear-depth group designs Collins and P
Reference 63
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Unavailable: canonical work link unavailable.
Observation c8ff3654-5870-4017-8189-abb267697a0e · outbound
No-go theorems for sublinear-depth group designs Collins and S
Reference 64
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 53d78663-5974-4c79-a44e-b7b4552204f7 · outbound
No-go theorems for sublinear-depth group designs Montealegre-Mora and D
Reference 65
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 f231f51d-2a3f-4b7f-b359-04714254a733 · outbound
No-go theorems for sublinear-depth group designs Zee,Group theory in a nutshell for physicists, Vol
Reference 66
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 543cdf7e-fa1a-4d5b-9638-ba16e65be9f6 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 67
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 78ac5f0b-f5fa-4e70-8e0b-8b6da38a0f6d · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 68
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 4548a0f5-7e47-4056-99f5-50f8b7c6d615 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 69
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 378c20dc-d237-4532-a2d6-b9b047509645 · outbound
No-go theorems for sublinear-depth group designs So, one guessesEwith probabilityp(ΠE|U∼X) = Tr[ρ X ΠE], whereρX = (ϕ(k) X ⊗I anc)(ρ)
Reference 70
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 a06abdf4-883c-4dfe-8c57-51c1b2dfda74 · outbound
No-go theorems for sublinear-depth group designs projectivelyG-invariant
Reference 71
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 3f5af7c4-8dd9-4395-82d6-affbcb9afe7c · outbound
No-go theorems for sublinear-depth group designs Consider any ensembleES N over elements of the formU= QN ℓ=1 exp(iθℓHℓ), where the generators are Paulis{Hℓ}ℓ⊂S⊂g
Reference 72
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 ea7fa755-dad8-4fb1-924f-000d7d81947f · outbound
No-go theorems for sublinear-depth group designs (9) by evaluating Eq
Reference 73
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 66ec9efd-32e0-4aef-9243-69f4ce6bead5 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 74
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 ae54c899-7c00-48f0-aaf4-2d3889a0b818 · outbound
No-go theorems for sublinear-depth group designs Note that from Eq
Reference 75
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 c891f441-d969-4851-9b25-d92eb5fa6806 · outbound
No-go theorems for sublinear-depth group designs Interestingly, and in contrast to the other groups we consider, we are here able to rule out sublinear-depth approximate designs only atk⩾8
Reference 76
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 19993228-cfb4-42f7-b596-34fe1bc9cee6 · outbound
No-go theorems for sublinear-depth group designs real”, “complex
Reference 77
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 dd71f05d-74d1-43d2-b485-29ff2aa5d15a · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 78
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 72c020c5-aae6-4d06-817f-d8aa27795281 · outbound
No-go theorems for sublinear-depth group designs Unresolved cited work
Reference 79
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 af939288-a411-44c2-bc23-ccb295684a76 · outbound
No-go theorems for sublinear-depth group designs HereχV = Tr◦RV :G→Cis thecharacterofV, i.e., the trace of the representing elementsR V :G→L(V)
Reference 80
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 5aad5bd1-3326-453f-94b9-65912d89524f · inbound
Apparent Universal Behavior in Second Moments of Random Quantum Circuits No-go theorems for sublinear-depth group designs
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 63c7e9bf-63c0-40be-85b7-538ab35ce4b3 · inbound
Classical shadows over symmetric spaces No-go theorems for sublinear-depth group designs
Reference 33
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a5ab8641-b746-4b3f-a3d6-6cc512b48752 · inbound
From Pauli Strings to Quantum Dynamics: A Unified Characterization No-go theorems for sublinear-depth group designs
Reference 229
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7d2af845-2ee5-4d48-be12-fa14c863834d · inbound
Particle-preserving fermionic shadows with mode-independent sample complexity No-go theorems for sublinear-depth group designs
Reference 35
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 7ea76b7e-a286-4758-9d83-7ca8eaf41f0e · inbound
Ambient unitaries don't enable shallow group designs No-go theorems for sublinear-depth group designs
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.