Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach | Paper Citation Record

Observation 6a971990-e3b4-483b-8b6a-c826ae9e2bf1 · outbound

This paper cites thermodynamic limit.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach thermodynamic limit

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Observation 3d8806cb-f1f6-4585-bfb7-a63adce7df12 · outbound

This paper cites [31] is that in each state trajectory of unitary circuit,g 3 al- ways changes by multiples of two.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach [31] is that in each state trajectory of unitary circuit,g 3 al- ways changes by multiples of two

Reference 2

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Observation d13da30b-3691-4ff3-b783-ff63b21ea0d3 · outbound

This paper cites Thus, the restriction of Γ to span{⃗ v,⃗ v∗,⃗ w,⃗ w∗}decomposes into two identical 2×2 blocks, each of rank 2.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Thus, the restriction of Γ to span{⃗ v,⃗ v∗,⃗ w,⃗ w∗}decomposes into two identical 2×2 blocks, each of rank 2

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This paper cites isolatedv 1.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach isolatedv 1

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Observation 09e0b0c6-fcea-4eef-b8c6-19587a86bbce · outbound

This paper cites dense” and “sparse.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach dense” and “sparse

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Observation 39f1d12d-f081-4c6a-8d74-aa365687a6c5 · outbound

This paper cites The same reasoning also applies to dynamics.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach The same reasoning also applies to dynamics

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Observation e31f83d0-94d8-4c65-9bd2-8af3dc1a857a · outbound

This paper cites It implies that the output state of a monitored random Clifford circuits can be un- 13 derstood as the output of a unitary Clifford cir- cuits overN sub qubits (see Sec.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach It implies that the output state of a monitored random Clifford circuits can be un- 13 derstood as the output of a unitary Clifford cir- cuits overN sub qubits (see Sec

Reference 7

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This paper cites interaction.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach interaction

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This paper cites 10(b): Assumingv 1 is a sparse vertex whilev 2 is dense, we need to determine the rate of infection by unitary gate.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach 10(b): Assumingv 1 is a sparse vertex whilev 2 is dense, we need to determine the rate of infection by unitary gate

Reference 9

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Observation a8f5237c-a6d6-42d4-b35f-184f28e7a112 · outbound

This paper cites The dynamics is controlled by a single parameterp∈[0,1], which tunes the recovery probability.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach The dynamics is controlled by a single parameterp∈[0,1], which tunes the recovery probability

Reference 10

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Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach interaction

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This paper cites This classifica- tion is proved to be useful as it helps us to quickly capture a series of important features.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach This classifica- tion is proved to be useful as it helps us to quickly capture a series of important features

Reference 13

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Observation f67cfdca-8420-4272-9251-cce587e77583 · outbound

This paper cites It enables the straightforward understanding of the volume- law phase by the relatively simpler unitary circuits.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach It enables the straightforward understanding of the volume- law phase by the relatively simpler unitary circuits

Reference 14

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This paper cites The model is perhaps over-simplified but it still captures the clustering of dense vertices and the MIPT in the form of an absorbing-state phase transition.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach The model is perhaps over-simplified but it still captures the clustering of dense vertices and the MIPT in the form of an absorbing-state phase transition

Reference 15

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This paper cites Then, a mean-field treatment of theC 1 tog- gles leads to an estimatep c = 0.1608, in excellent agreement with numerical simulations.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Then, a mean-field treatment of theC 1 tog- gles leads to an estimatep c = 0.1608, in excellent agreement with numerical simulations

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This paper cites Stabilizers of the post-measurement states (I± P1)|Γ⟩are different by some signs.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Stabilizers of the post-measurement states (I± P1)|Γ⟩are different by some signs

Reference 18

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This paper cites This operation is based on the formula [84] HaHb|Γ⟩=Z aZb Y i∈µ∗(x) Y j∈µ∗(y) CZi,j|Γ⟩,(B12) which is conditioned on (va,vb) is connected.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach This operation is based on the formula [84] HaHb|Γ⟩=Z aZb Y i∈µ∗(x) Y j∈µ∗(y) CZi,j|Γ⟩,(B12) which is conditioned on (va,vb) is connected

Reference 19

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Observation 6e0f4827-1f18-481c-9cd6-e9fa90ef60e3 · outbound

This paper cites The Heisenberg Representation of Quantum Computers.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach The Heisenberg Representation of Quantum Computers

Reference 21

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This paper cites Aaronson and D.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Aaronson and D

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This paper cites Anders and H.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Anders and H

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This paper cites Skinner, J.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Skinner, J

Reference 26

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This paper cites Szyniszewski, A.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Szyniszewski, A

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This paper cites Nahum, S.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Nahum, S

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This paper cites Block, Y.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Block, Y

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This paper cites Sharma, X.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Sharma, X

Reference 30

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This paper cites Lavasani, Y.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Lavasani, Y

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Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Lavasani, Y

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This paper cites Ippoliti and V.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Ippoliti and V

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Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Lu and T

Reference 34

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This paper cites Ippoliti, T.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Ippoliti, T

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This paper cites Turkeshi, R.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Turkeshi, R

Reference 36

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Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Sierant, M

Reference 37

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This paper cites Measurement-induced entanglement in noisy 2D random circuits.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Measurement-induced entanglement in noisy 2D random circuits

Reference 40

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This paper cites Li and M.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Li and M

Reference 43

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Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Ippoliti, M

Reference 46

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This paper cites Lavasani, Y.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Lavasani, Y

Reference 47

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This paper cites Sang and T.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Sang and T

Reference 48

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This paper cites Morral-Yepes, F.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Morral-Yepes, F

Reference 49

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This paper cites Xu and Y.-X.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Xu and Y.-X

Reference 50

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This paper cites Sharma and E.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Sharma and E

Reference 51

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Reference 52

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Observation a2475301-7746-4a46-be6b-b8db521529d8 · outbound

This paper cites Bejan, C.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Bejan, C

Reference 53

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This paper cites Scocco, W.-K.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Scocco, W.-K

Reference 54

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Observation faa2d81f-364d-4c68-b8a1-9a43dbea6c8f · outbound

This paper cites Nahum, J.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Nahum, J

Reference 56

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This paper cites Weingarten Calculus.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Weingarten Calculus

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This paper cites Jian, Y.-Z.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Jian, Y.-Z

Reference 59

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This paper cites Zhou and A.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Zhou and A

Reference 60

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Observation 304cdc93-a519-45d8-abf2-9bf9bf70e03c · outbound

This paper cites Gross, S.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Gross, S

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.385299Z

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Observation bedd4f93-3a36-4c97-8db2-24fb46146f78 · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.389124Z

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Observation f472f1c3-7ede-430e-b97a-74cb7e9d3824 · outbound

This paper cites Zhu, Multiqubit clifford groups are unitary 3-designs, Phys.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Zhu, Multiqubit clifford groups are unitary 3-designs, Phys

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Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.392830Z

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Observation e191928c-bb57-48cf-b5a7-a937e4705d11 · outbound

This paper cites Halpin-Healy and Y.-C.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Halpin-Healy and Y.-C

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:03.163763Z

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

Observation 2d5cd4e8-85d2-449f-89f8-50f2a51c4aab · outbound

This paper cites Kardar, G.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Kardar, G

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.400208Z

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Observation 4d724ffd-4379-479f-938a-9f60dc04a936 · outbound

This paper cites Nezami and M.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Nezami and M

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.404303Z

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Observation 26d934cc-fdd0-4104-873f-98c8fb7b219f · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 67

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:04:03.133343Z

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Observation bd0a1adc-fbd0-447c-a28f-265bda070aa1 · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 68

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:04:03.121364Z

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Observation bfc770b5-1bb0-42d6-9aa5-88f40282d078 · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.416161Z

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Observation f553dbdc-7b66-4115-9281-089f7e42ec17 · outbound

This paper cites Sheffer, A.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Sheffer, A

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.419985Z

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Observation c2a10ba1-7599-4212-8a8d-34e862cbbd10 · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 71

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:04:03.090107Z

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Observation fab3ff81-0992-4d53-b7eb-992624febc46 · outbound

This paper cites Network-Irreducible Multiparty Entanglement in Quantum Matter.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Network-Irreducible Multiparty Entanglement in Quantum Matter

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.427530Z

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Observation 12a88570-bb09-4b52-bc9f-f5c3b268d390 · outbound

This paper cites Operational meaning of Markov gap in tripartite entanglement of quantum dynamics.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Operational meaning of Markov gap in tripartite entanglement of quantum dynamics

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Resolution: verified exact; local_arxiv, observed 2026-08-15T15:04:02.692745Z

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

Observation 6be417c6-9356-44ba-9002-a53a83e20194 · outbound

This paper cites Akers and P.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Akers and P

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:03.075571Z

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Observation 64046018-7e1d-4df0-a12c-7768b93af2f0 · outbound

This paper cites Hayden, O.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Hayden, O

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:03.059197Z

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Observation 2dfc092f-c9b4-4122-979f-01c267e94d4b · outbound

This paper cites Balasubramanian, M.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Balasubramanian, M

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:03.045164Z

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Observation e94b2fa6-a142-4d2b-9679-6280dff2e147 · outbound

This paper cites Iizuka, A.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Iizuka, A

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:03.028953Z

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Observation 961001cb-1284-47a8-b9b4-24c692cf4bd3 · outbound

This paper cites Gadde, V.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Gadde, V

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:03.015039Z

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Observation 0ab7d556-71e6-426f-a574-9060c4995f61 · outbound

This paper cites Akers, R.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Akers, R

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.455173Z

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Observation 5568cfe4-61a2-4787-8b85-807ed6212f74 · outbound

This paper cites Genuine multi-entropy and holography.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Genuine multi-entropy and holography

Reference 80

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.458953Z

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Observation 88fa8cf5-2715-4c82-a51e-1ff3315bc12d · outbound

This paper cites More on genuine multi-entropy and holography.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach More on genuine multi-entropy and holography

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.464274Z

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Observation 29c3c720-c7c7-4b69-8b7d-91531eb4bd74 · outbound

This paper cites Balasubramanian, M.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Balasubramanian, M

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:02.989523Z

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Observation 40cf3272-e214-43e8-b0ba-fbe0982190da · outbound

This paper cites Lira-Solanilla, X.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Lira-Solanilla, X

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.472341Z

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Observation 0f7f10fe-e939-4b3b-a76d-948a5d9e9f30 · outbound

This paper cites Entanglement in the stabilizer formalism.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Entanglement in the stabilizer formalism

Reference 84

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.476718Z

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Observation 4d2c2f79-c6f8-4c4d-8b9f-5998c3018f0d · outbound

This paper cites Bravyi, D.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Bravyi, D

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:02.972708Z

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Observation 3661e0ca-7311-43ca-872b-99d46bdf9baf · outbound

This paper cites Smith and D.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Smith and D

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.484417Z

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Observation a2d4e3b9-2f59-40e7-af96-4b6ef5107eed · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 87

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.488268Z

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Observation 22aec9ae-b6b9-43be-b57d-455db67a45ce · outbound

This paper cites Bertini, K.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Bertini, K

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:02.941936Z

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Observation 0978e151-e7aa-4d0f-90c7-29b497bfe352 · outbound

This paper cites Vidal and R.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Vidal and R

Reference 89

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.496151Z

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Observation b4e74403-ca6a-4016-aa76-0f517640cea4 · outbound

This paper cites Calabrese and J.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Calabrese and J

Reference 90

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.499912Z

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Observation ac18efe9-3fa7-4487-a4bd-2b219ae67ca6 · outbound

This paper cites Calabrese, J.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Calabrese, J

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:02.913199Z

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Observation 9369fad9-3eda-479d-ab42-95b9601868fe · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 92

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:04:02.900397Z

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Observation aa70a2e9-0c86-49bd-b2c4-ed9c37040fbe · outbound

This paper cites Weinstein, Y.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Weinstein, Y

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:02.887242Z

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

Observation 007e06fe-cf52-4b6b-9e50-0ba02422d25c · outbound

This paper cites Schlingemann and R.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Schlingemann and R

Reference 94

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.515025Z

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Observation 98d4531f-c013-42b3-bbf2-b5301c076f6f · outbound

This paper cites Raussendorf, D.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Raussendorf, D

Reference 95

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.519029Z

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Observation df5eebd5-c71e-4589-8d02-3fbec915c122 · outbound

This paper cites Kotzig, Eulerian lines in finite 4-valent graphs and their transformations., Colloqium on Graph Theory Ti- hany 1966 , 219 (1968).

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Kotzig, Eulerian lines in finite 4-valent graphs and their transformations., Colloqium on Graph Theory Ti- hany 1966 , 219 (1968)

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:02.857042Z

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 08634119-dc4c-4dee-b926-972dc6b7142e · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 97

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:04:02.844074Z

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Observation 51552612-846e-41fb-bbd6-4b1fc869ba26 · outbound

This paper cites Erd¨ os and A.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Erd¨ os and A

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:04:02.831032Z

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 0f0d18de-b7ff-49d3-856b-dbe23c7ae2a7 · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 99

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:04:02.818026Z

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Observation 79c3e70c-7c6b-489a-97ca-8619641918af · outbound

This paper cites an unresolved cited work.

Typical Output States of Monitored Random Clifford Circuits: A Graph-Theoretic Approach Unresolved cited work

Reference 100

Resolution: unresolved; no resolver link, observed 2026-08-15T15:04:02.541140Z

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