Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T16:18:25.503748Z
Paper Citation Record · LEDGER
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths
As of 13 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2411.13739.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-04T07:56:55.204901Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
24 of 24 outbound references displayed
- verified exact0
- verified fuzzy23
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b925f21b-4b4c-45a9-ba1b-797c351f7c14 · outbound
This paper cites Isakov, Vadim N.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Isakov, Vadim N
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:27.352222Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 915655e3-677d-498c-9928-378271cd3a99 · outbound
This paper cites Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G.S.L.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G.S.L
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:27.253641Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f765375c-8ebe-433d-bc12-4a6bbfe415f8 · outbound
This paper cites Quantum supremacy and random circuits.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Quantum supremacy and random circuits
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:27.246221Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation dd8722fb-0e22-452c-8cca-fbe6816c3993 · outbound
This paper cites Brown and Leonard Susskind.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Brown and Leonard Susskind
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:27.237993Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7180b3dd-d1d2-4626-9be9-db36c6b10845 · outbound
This paper cites Black holes as mirrors: Quantum information in random subsystems.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Black holes as mirrors: Quantum information in random subsystems
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:27.149629Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation e18f40b4-905f-487b-9475-ef7b9a938448 · outbound
This paper cites Measurement-Induced Phase Transitions in the Dynamics of Entanglement.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Measurement-Induced Phase Transitions in the Dynamics of Entanglement
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:27.111434Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation be7f2e1d-dea7-4415-8daf-7bef9d23861a · outbound
This paper cites Theory of the phase transition in random unitary circuits with measure- ments.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Theory of the phase transition in random unitary circuits with measure- ments
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:27.053361Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 61740807-7ed5-4128-bdba-30d565722dc5 · outbound
This paper cites Lykken, David K.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Lykken, David K
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.916174Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 513001aa-28f4-4939-b3fa-aa2bfea6b0d4 · outbound
This paper cites Brand˜ ao, Aram W.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Brand˜ ao, Aram W
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.851779Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1ab53fad-9340-41b6-a0f5-7c5edf789f7e · outbound
This paper cites Random quantum circuits are approximate unitary t-designs in depth O(nt5+o(1)).
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Random quantum circuits are approximate unitary t-designs in depth O(nt5+o(1))
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.686640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f964b7de-fc0c-4318-aee1-f3eba8d0777d · outbound
This paper cites Incompressibility and spectral gaps of random circuits.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Incompressibility and spectral gaps of random circuits
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.646074Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 15e94189-55f1-44f3-98f9-c12089e519ef · outbound
This paper cites Random unitaries in extremely low depth.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Random unitaries in extremely low depth
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.551199Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation da05d119-a0f5-4b2c-a9b6-88cb0304ce5a · outbound
This paper cites Approximate Unitary k-Designs from Shallow, Low-Communication Circuits.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Approximate Unitary k-Designs from Shallow, Low-Communication Circuits
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.457245Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 0ce0b314-d639-4167-b218-96dcc7d90f5d · outbound
This paper cites an unresolved cited work.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T16:18:26.352621Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b3201a2f-2630-4d60-b392-1a55d485c6f4 · outbound
This paper cites Dalzell, Nicholas Hunter-Jones, and Fernando G.S.L.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Dalzell, Nicholas Hunter-Jones, and Fernando G.S.L
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.270777Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 29846ad9-0c98-4b19-ae2e-020c01223279 · outbound
This paper cites Deneris, Pablo Bermejo, Paolo Braccia, Lukasz Cincio, and Marco Cerezo.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Deneris, Pablo Bermejo, Paolo Braccia, Lukasz Cincio, and Marco Cerezo
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.226154Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ea212dd8-4d72-461e-90aa-29eb50f00ace · outbound
This paper cites Improved spectral gaps for random quantum circuits: Large local dimen- sions and all-to-all interactions.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Improved spectral gaps for random quantum circuits: Large local dimen- sions and all-to-all interactions
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.104256Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 94e6cc51-09a6-45c3-a3c8-6732849eb82e · outbound
This paper cites Unitary designs from statistical mechanics in random quantum circuits.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Unitary designs from statistical mechanics in random quantum circuits
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:26.037372Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 584c4f7e-1749-4ca5-a28f-8f0039cda1bb · outbound
This paper cites Solvable non-Hermitian skin effect in many-body unitary dynamics.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Solvable non-Hermitian skin effect in many-body unitary dynamics
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:25.933591Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f04443d4-59e0-4f51-b802-58b933d10d01 · outbound
This paper cites Integration with respect to the Haar measure on unitary, orthogonal and symplectic group.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:25.814926Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 3e364566-7d4a-4864-8216-7d7eac21dabb · outbound
This paper cites Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:25.770574Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 28e3887d-3f2f-4cc0-8736-da8dc114dd96 · outbound
This paper cites Jucys-Murphy elements and weingarten matrices.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths Jucys-Murphy elements and weingarten matrices
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:25.715769Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 06c70940-5697-4216-8ffc-15003bd8198b · outbound
This paper cites even” and “odd.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths even” and “odd
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T16:18:25.624590Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 38fbcb6a-9996-43fd-9c7c-a1042cae2f20 · outbound
This paper cites 1 2 + 3 t t + 4√ t t# (232) Furthermore, when t ≤ q, this bound can be simplified to dt(q−2) ≤ t2 2 e 1 2t2.
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths 1 2 + 3 t t + 4√ t t# (232) Furthermore, when t ≤ q, this bound can be simplified to dt(q−2) ≤ t2 2 e 1 2t2
Reference 24
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- raw_fallback, observed 2026-08-12T16:18:25.558014Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
Observation a7fedc3a-e49e-4a84-9a26-284c896b4d2d · inbound
Apparent Universal Behavior in Second Moments of Random Quantum Circuits cites this paper.
Apparent Universal Behavior in Second Moments of Random Quantum Circuits Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T07:56:55.204901Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.