Paper Citation Record · LEDGER

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions

As of 17 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2501.04091.

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

pith.paper-citation-record.v1
2501.04091 v3

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:48:15.228148Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact1
verified fuzzy16
unresolved19
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f95aad2a-5dda-4f9b-9dfe-bccec1c65659 · outbound

This paper cites Scrambling speed of random quantum circuits.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Scrambling speed of random quantum circuits

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.072005Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3b3d416-2af5-4a76-99f8-2f37ec1db75d · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.724939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e9204a60-2f2c-42a0-be69-fbc6523ac13c · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.690216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4adbf731-9b82-4c66-bb3f-0c42aff80792 · outbound

This paper cites Nahum, J.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Nahum, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.707076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6c38c6dc-2bf0-47da-b181-1946fdd40160 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.089819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 214dad51-2d57-4d72-8eea-1915791ee65a · outbound

This paper cites Nahum, S.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Nahum, S

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.675524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 77a3f1a1-7a3c-4ea4-90d7-f23f0d70c800 · outbound

This paper cites Khemani, A.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Khemani, A

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.642181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3a5c9851-90be-4f89-a1ea-34aec4415855 · outbound

This paper cites Rakovszky, F.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Rakovszky, F

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.655670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e243c3e0-5cd5-437e-8aad-622f34597de0 · outbound

This paper cites Lecture Notes: Introduction to random unitary circuits and the measurement-induced entanglement phase transition.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Lecture Notes: Introduction to random unitary circuits and the measurement-induced entanglement phase transition

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.109219Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43586a15-dc77-4c08-a82b-d2bc499ae72a · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.104893Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5af5978b-a92e-4d3a-bf0a-e1d358df7293 · outbound

This paper cites Styliaris, N.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Styliaris, N

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.610101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f8489359-2cfd-4e26-9841-b94b2525cfb3 · outbound

This paper cites Xu and B.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Xu and B

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.115029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4b53b33-c48c-4599-82e1-599f787c1027 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.582623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ea2f7884-1e70-4713-ab63-add791c00cf8 · outbound

This paper cites Xu and B.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Xu and B

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.597055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3f74ef09-a0d8-47d6-bcff-44fb5c7ef5b0 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.557769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 144efea0-a728-4c89-b32b-ab424a4ec616 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.569835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ddf7d9fc-e55e-4b93-84bc-9bcda1accfdc · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.529768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4182265f-8c80-43ef-ae9c-59563a237fae · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.544858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 33d54eef-339f-406e-a06e-6eb92582c5a1 · outbound

This paper cites Operator growth in random quantum circuits with symmetry.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Operator growth in random quantum circuits with symmetry

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.152799Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84bb093a-3480-4404-9205-661e5a6e00e0 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.513365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3cf00945-598c-4ea4-9fc7-e013dcac8921 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.483780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 762c869a-a3b6-44d2-aa00-d17fd4f51df5 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.497952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 41b0b354-9c61-4c25-bd81-4475cb122581 · outbound

This paper cites Patera and H.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Patera and H

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.467161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation dd1bfa68-a7c1-40f6-a454-b36cb3f8eb6b · outbound

This paper cites Following Ref.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Following Ref

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.739896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f065714d-15df-4d66-b97e-08c072f55c67 · outbound

This paper cites Brownian Gaussian Unitary Ensemble: non-equilibrium dynamics, efficient $k$-design and application in classical shadow tomography.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Brownian Gaussian Unitary Ensemble: non-equilibrium dynamics, efficient $k$-design and application in classical shadow tomography

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-10T21:48:15.273102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c9d8b003-1222-4288-8030-48cd71af3a76 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:48:15.453827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 545cc51d-7531-4fe7-90b5-28f75e0ccebd · outbound

This paper cites Weingarten, Asymptotic behavior of group integrals in the limit of infinite rank, J.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Weingarten, Asymptotic behavior of group integrals in the limit of infinite rank, J

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.181985Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26014258-3096-483d-bb51-74be2b82e754 · outbound

This paper cites Collins, Moments and Cumulants of Polynomial Random 21 Variables on Unitary Groups, the Itzykson-Zuber Integral, and Free Probability, Int.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Collins, Moments and Cumulants of Polynomial Random 21 Variables on Unitary Groups, the Itzykson-Zuber Integral, and Free Probability, Int

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.431669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4cc5bd81-041f-4cde-9435-d9e65e44cc5f · outbound

This paper cites Chen and E.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Chen and E

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.419407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b7eaa171-1004-4644-a845-d3c27c25b7ee · outbound

This paper cites Henderson, E.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Henderson, E

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.407812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5b3fc602-1cb6-40a9-998b-325df3beb406 · outbound

This paper cites Renshaw and R.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Renshaw and R

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.395180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 721a29d8-46a4-45b9-abe9-8b6450dad9a0 · outbound

This paper cites Pandey and P.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Pandey and P

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.382392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d199699e-78be-432f-916a-b5734d718f67 · outbound

This paper cites an unresolved cited work.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-10T21:48:15.212972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15151ce6-7e29-42f7-b63e-de8f7495f08a · outbound

This paper cites Diaconis and S.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Diaconis and S

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.361900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 333b1c6c-f762-4164-86f5-6853ca12b161 · outbound

This paper cites Johansson, On Random Matrices from the Compact Classi- cal Groups, Ann.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Johansson, On Random Matrices from the Compact Classi- cal Groups, Ann

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.347615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e3ec1751-b299-4a6f-aa3a-cd7dbac5fea9 · outbound

This paper cites Fulton and J.

Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions Fulton and J

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:48:15.331783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

No inbound Pith citation observations are available.