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Paper Citation Record · LEDGER

Hardness and Complexity Transition of Noisy Random Circuit Sampling

As of 17 August 2026, this Paper Citation Record lists 85 of 85 outbound references and 0 inbound Pith citation observations for arXiv:2607.20804.

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

pith.paper-citation-record.v1
2607.20804 v1

Coverage vector

measured 85 of 85 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T09:31:34.189845Z

measured 85 of 85 standing notices

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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.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

85 of 85 outbound references displayed

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  • unresolved85
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Outbound references

Observation ec7a1c23-597b-4c9a-bec6-9f01d985a160 · outbound

This paper cites Subsequently, Ref.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Subsequently, Ref

Reference 1

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Observation 0c84b758-8f2d-41d8-95cb-8ec723d8a436 · outbound

This paper cites Noise and the frontier of quantum supremacy.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Noise and the frontier of quantum supremacy

Reference 2

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Observation b4cd1b81-8911-4a03-974f-08be61762f42 · outbound

This paper cites an unresolved cited work.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Unresolved cited work

Reference 3

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Observation e2ac32e4-cfc7-4cae-8124-69bca9a8b246 · outbound

This paper cites VII, we conclude with remarks and directions for future work.

Hardness and Complexity Transition of Noisy Random Circuit Sampling VII, we conclude with remarks and directions for future work

Reference 4

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Observation 88f7aba8-06e1-4077-9e09-213ad03a5d4d · outbound

This paper cites Average-case hardness of estimating probabilities of random quantum circuits with a linear scaling in the error exponent.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Average-case hardness of estimating probabilities of random quantum circuits with a linear scaling in the error exponent

Reference 5

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Observation 54a21c5d-429c-4570-b978-b85217307722 · outbound

This paper cites ( 10), respectively.

Hardness and Complexity Transition of Noisy Random Circuit Sampling ( 10), respectively

Reference 6

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Observation 415e57dc-4ee2-4319-99ba-e2e62976ccb3 · outbound

This paper cites simulation.

Hardness and Complexity Transition of Noisy Random Circuit Sampling simulation

Reference 7

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source=pdf_text observed=2026-08-01T09:31:33.306424Z digest=sha256:e28494b3ee9fe903b8031cda0f27fd5cd1b12c23eb2fd1faa9090518153aacf3

Observation 4d9d0261-851e-4063-ac21-63dfbfe9e685 · outbound

This paper cites Quantum computational advantage via 60-qubit 24-cycle random circuit sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Quantum computational advantage via 60-qubit 24-cycle random circuit sampling

Reference 8

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Observation a124300e-3bd7-41c6-aa4f-eb313dd1d61d · outbound

This paper cites Phase transitions in random circuit sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Phase transitions in random circuit sampling

Reference 9

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Observation e5119f6d-068e-474c-94e4-75af543b5f19 · outbound

This paper cites Computational power of random quantum circuits in arbitrary geometries.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Computational power of random quantum circuits in arbitrary geometries

Reference 10

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Observation c6578233-59ae-48ad-ba89-9814f88bdb9c · outbound

This paper cites On the complexity and verification of quantum random circuit sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling On the complexity and verification of quantum random circuit sampling

Reference 11

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Observation 0060902d-b2df-41e3-897b-91fa173d7c84 · outbound

This paper cites Limitations of Noisy Reversible Computation.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Limitations of Noisy Reversible Computation

Reference 12

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Observation 69b33aba-5145-4cbf-95fc-fba5547b5b6c · outbound

This paper cites Thus, under Conjecture 1, this yields the #P-hardness claimed in Theorem 2.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Thus, under Conjecture 1, this yields the #P-hardness claimed in Theorem 2

Reference 13

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Observation 6a0febc2-b692-4a45-b992-a2fbe89c5fce · outbound

This paper cites Quantum supremacy and hardness of estimating output probabilities of quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Quantum supremacy and hardness of estimating output probabilities of quantum circuits

Reference 14

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source=pdf_text observed=2026-08-01T09:31:33.406821Z digest=sha256:bb6b65a29f50cdf42b5f69ae12f1122f0ebab6f2d32c318b6cc56192598fd057

Observation 8ec9d64d-288f-4990-85cd-dce4f87b2ee5 · outbound

This paper cites an unresolved cited work.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Unresolved cited work

Reference 15

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Observation 5ecba682-2adf-4b6b-a07c-eff3121201b5 · outbound

This paper cites (15) for each fixed γ ∈ [0, γmax] by Pr C∼HA [ |˜p(C, γ) −˜pl(C, γ)| > ε′ 2n ] ≤ δ, (18) where the approximation error ε′ can be chosen as ε′ := 4N 2γmax lδ ( 3e N γmax 8l ) l.

Hardness and Complexity Transition of Noisy Random Circuit Sampling (15) for each fixed γ ∈ [0, γmax] by Pr C∼HA [ |˜p(C, γ) −˜pl(C, γ)| > ε′ 2n ] ≤ δ, (18) where the approximation error ε′ can be chosen as ε′ := 4N 2γmax lδ ( 3e N γmax 8l ) l

Reference 16

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Observation 36a7fe36-7d32-4d16-8032-d6993081191c · outbound

This paper cites The hardness of random quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling The hardness of random quantum circuits

Reference 17

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Observation 4a424641-70a5-4a68-bfb5-870b56539a6a · outbound

This paper cites Quantum supremacy using a programmable superconducting processor.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Quantum supremacy using a programmable superconducting processor

Reference 18

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Observation e8208697-75d7-4926-97b5-3728b065e783 · outbound

This paper cites Strong quantum computational advantage using a superconducting quantum processor.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Strong quantum computational advantage using a superconducting quantum processor

Reference 19

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Observation 665e5a57-8504-4fec-ba61-a652f1c945f2 · outbound

This paper cites Classically sampling noisy quantum circuits in quasi-polynomial time under approximate markovianity.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classically sampling noisy quantum circuits in quasi-polynomial time under approximate markovianity

Reference 20

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Observation 45a5e757-963a-48cc-a456-79851077e06a · outbound

This paper cites Establishing a new benchmark in quantum computational advantage with 105-qubit zuchongzhi 3.0 processor.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Establishing a new benchmark in quantum computational advantage with 105-qubit zuchongzhi 3.0 processor

Reference 21

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Observation ed55b950-6dbf-4bfd-a7e2-6816d2e3ea47 · outbound

This paper cites Noisy random quantum circuit sampling and its classical simulation.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Noisy random quantum circuit sampling and its classical simulation

Reference 22

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Observation d6b6e23f-157c-4017-aba6-6714634082d4 · outbound

This paper cites Efficient classical simulation of noisy quantum computation.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient classical simulation of noisy quantum computation

Reference 23

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Observation 7876adb9-66fa-4486-ba9b-3a70cd576201 · outbound

This paper cites Tight bounds on the convergence of noisy random circuits to the uniform distribution.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Tight bounds on the convergence of noisy random circuits to the uniform distribution

Reference 24

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Observation 74b101e5-79f1-4a0c-831d-5ba55efb60c6 · outbound

This paper cites A polynomial-time classical algorithm for noisy random circuit sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling A polynomial-time classical algorithm for noisy random circuit sampling

Reference 25

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Observation 08bf449d-79f5-4803-986c-beded148c10f · outbound

This paper cites Random quantum circuits transform local noise into global white noise.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Random quantum circuits transform local noise into global white noise

Reference 26

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Observation 571560a7-923a-4b8f-bcfb-1a235f78a37c · outbound

This paper cites Limitations of noisy geometrically local quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Limitations of noisy geometrically local quantum circuits

Reference 27

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Observation b1920603-de47-436f-8dab-d8b4bc92dddc · outbound

This paper cites Polynomial-time classical simulation of noisy quantum circuits with naturally fault-tolerant gates.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Polynomial-time classical simulation of noisy quantum circuits with naturally fault-tolerant gates

Reference 28

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Observation 33c8a5d8-72f4-48a7-869a-5b89a72972c9 · outbound

This paper cites By construction, ¯p(C, γ2, x) = E s∼wγadd [ ¯p(Cs, γ1, x)].

Hardness and Complexity Transition of Noisy Random Circuit Sampling By construction, ¯p(C, γ2, x) = E s∼wγadd [ ¯p(Cs, γ1, x)]

Reference 29

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Observation 1f74e206-527a-43de-bd3a-b1af82dc7470 · outbound

This paper cites Classical simulation of noisy random circuits from exponential decay of correlation.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulation of noisy random circuits from exponential decay of correlation

Reference 30

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Observation 296e6cd1-1a54-4c9c-8753-7b386b336667 · outbound

This paper cites Efficient classical simulation of noisy random quantum circuits in one dimension.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient classical simulation of noisy random quantum circuits in one dimension

Reference 31

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Observation 869d7baa-364a-4134-91bd-f118d0a34b9f · outbound

This paper cites Density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity

Reference 32

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Observation ed48eb4b-0d00-4562-9601-ce8e5dcf6cbf · outbound

This paper cites Classical Simulation of Intermediate-Size Quantum Circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical Simulation of Intermediate-Size Quantum Circuits

Reference 33

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Observation c17cdc43-a97f-4f5b-b90e-78da8f95b6f1 · outbound

This paper cites A Fourier analysis framework for approximate classical simulations of quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling A Fourier analysis framework for approximate classical simulations of quantum circuits

Reference 34

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source=pdf_text observed=2026-08-01T09:31:33.662320Z digest=sha256:e9ade56c65b5204eab4be70172731c25541bd9456814102daf9602359895de77

Observation bfab0a63-2dc6-4f8c-99da-c1cf2a1bff77 · outbound

This paper cites Classical Simulation of Quantum Supremacy Circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical Simulation of Quantum Supremacy Circuits

Reference 35

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Observation f65bd98e-f469-4c94-bfb7-a35a3c11656f · outbound

This paper cites Computational advantage of quantum random sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Computational advantage of quantum random sampling

Reference 36

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Observation b6a8c17c-cf7e-48f8-bc1e-40b843c6e873 · outbound

This paper cites A polynomial-time classical algorithm for noisy quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling A polynomial-time classical algorithm for noisy quantum circuits

Reference 37

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source=pdf_text observed=2026-08-01T09:31:33.701578Z digest=sha256:1d0545d946b1d67e9cf766cabf0836eb939c3ecbec601e9aa8681010bb169ea7

Observation f9bd99d8-9871-4387-be7e-1b47c434f92e · outbound

This paper cites Simulation of quantum circuits using the big-batch tensor network method.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Simulation of quantum circuits using the big-batch tensor network method

Reference 38

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source=pdf_text observed=2026-08-01T09:31:33.710409Z digest=sha256:d6ddad866a29fae96e6dad16fe2d5e44ecaae45074c6d1b1a6cf097b7de831d3

Observation 30f49c3a-cbe5-45ff-8704-7fad17e66bff · outbound

This paper cites Classical simulations 20 of noisy variational quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulations 20 of noisy variational quantum circuits

Reference 39

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source=pdf_text observed=2026-08-01T09:31:33.720224Z digest=sha256:e5a00cb7f9e4b1cc8e5ce15af064990baf3f355670d0966cafb5575b35ee1f41

Observation 3e814de6-4813-4fd3-a02f-d421863aab43 · outbound

This paper cites Enabling large-depth simulation of noisy quantum circuits with positive tensor networks.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Enabling large-depth simulation of noisy quantum circuits with positive tensor networks

Reference 40

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source=pdf_text observed=2026-08-01T09:31:33.724640Z digest=sha256:0e7975b5f6c9c31dd2c71a64ee066ee0d724270a5f09e1a2e37c5b304c813963

Observation f0327402-017f-4e3c-bcf2-c51a901ea2ca · outbound

This paper cites Simulating noisy quantum circuits with matrix product density operators.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Simulating noisy quantum circuits with matrix product density operators

Reference 41

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source=pdf_text observed=2026-08-01T09:31:33.732993Z digest=sha256:6da20f23816614fbfc6cbf5348116bc6b37ef82e9859cfdb781096bd46e4535c

Observation 000ec9b0-e274-4582-9e0c-8084df9b6117 · outbound

This paper cites an unresolved cited work.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Unresolved cited work

Reference 42

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source=pdf_text observed=2026-08-01T09:31:33.352478Z digest=sha256:ca7c0a79024fb7cee671513f97cdcd964c3001e197646b6b7cd21aebcd83e0c2

Observation fcbd34d2-b609-47ec-b172-d9bbc9ff59c3 · outbound

This paper cites Scalable projected entangled-pair state representation of random quantum circuit states.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Scalable projected entangled-pair state representation of random quantum circuit states

Reference 43

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source=pdf_text observed=2026-08-01T09:31:33.748719Z digest=sha256:12d20f25c428d9f5fec7945f469625049eaa59c464302c85ae899b8316407ba3

Observation 793ce953-b17e-4d8d-be31-6b8ae194123a · outbound

This paper cites Relative entropy convergence for depolarizing channels.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Relative entropy convergence for depolarizing channels

Reference 44

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source=pdf_text observed=2026-08-01T09:31:33.754951Z digest=sha256:197b6359e60d7d80ad65aabc49fad3bdaca4a7a3f99823e37a25267dcfefb4f5

Observation 4a76f173-c592-436d-aa96-57bb337fa20a · outbound

This paper cites Noise-induced shallow circuits and absence of barren plateaus.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Noise-induced shallow circuits and absence of barren plateaus

Reference 45

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source=pdf_text observed=2026-08-01T09:31:33.762442Z digest=sha256:a9735dfac6eea272ae608296ace71368dd55c315085c0827bf6cb44567119fef

Observation 19985060-b80b-45fe-90f5-9a1cf3221213 · outbound

This paper cites Limitations of optimization algorithms on noisy quantum devices.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Limitations of optimization algorithms on noisy quantum devices

Reference 46

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source=pdf_text observed=2026-08-01T09:31:33.774011Z digest=sha256:98ea4e46b7bc441b11018b9d33e3f18d2c417b5a49e5477bebe0b83f717505af

Observation 7147ef85-f91d-411d-9592-503e47541cc4 · outbound

This paper cites Efficient classical simulation of random shallow 2d quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient classical simulation of random shallow 2d quantum circuits

Reference 47

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source=pdf_text observed=2026-08-01T09:31:33.782083Z digest=sha256:21a82a919c1bc516e0b0ace631311e7237663f370ca79925eb3ea20fa5b2077b

Observation 85989711-1d34-468a-9399-bba9fbab96f4 · outbound

This paper cites Efficient sampling of noisy shallow circuits via monitored unraveling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient sampling of noisy shallow circuits via monitored unraveling

Reference 48

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source=pdf_text observed=2026-08-01T09:31:33.791641Z digest=sha256:4e8e22e7440e9a8ee2ca52194d1158ea925de648d2708430b816a31f1e22ed02

Observation c0c6b4be-9771-4616-81c2-5bc0f8bdd391 · outbound

This paper cites Optimized trajectory unraveling for classical simulation of noisy quantum dynamics.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Optimized trajectory unraveling for classical simulation of noisy quantum dynamics

Reference 49

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source=pdf_text observed=2026-08-01T09:31:33.796221Z digest=sha256:95948552e365ba6602a3f371323824e9fc3083ddc9c4b8fa14721b87f65e741f

Observation 188b53da-98d7-479a-bb0d-38391c544ead · outbound

This paper cites Efficient simulation of one-dimensional quantum many-body systems.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient simulation of one-dimensional quantum many-body systems

Reference 50

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source=pdf_text observed=2026-08-01T09:31:33.800867Z digest=sha256:a2b9e34ff18e9f5c2265c2b2d73402435fce391895f41ef54f4bdb6e957dd21a

Observation bd44780c-10fb-40c5-8ac7-0f96e21826aa · outbound

This paper cites Simulating quantum computation by contracting tensor networks.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Simulating quantum computation by contracting tensor networks

Reference 51

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source=pdf_text observed=2026-08-01T09:31:33.807956Z digest=sha256:8b514f2add793ed2f094127d19640cfb488d02cf0ad15e0ed1dd463c34917a56

Observation c97059cc-63ef-4bec-a1f3-cc2584355e99 · outbound

This paper cites On the simulation of quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling On the simulation of quantum circuits

Reference 52

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source=pdf_text observed=2026-08-01T09:31:33.816222Z digest=sha256:b50f1e41722c98774d4a7e89f980f0b4dd37b6bda517272449652e0015dfbd39

Observation 320fff38-51b5-4b81-8e47-755498e2e697 · outbound

This paper cites On approximation algorithms for# p.

Hardness and Complexity Transition of Noisy Random Circuit Sampling On approximation algorithms for# p

Reference 53

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source=pdf_text observed=2026-08-01T09:31:33.824726Z digest=sha256:9de64602cf2de1656b2f0d73692bcf10b5661ca06ea9a2afa571a67e9f82e8ff

Observation eaf086b4-a4a0-4f3f-b0ce-fe6185bad682 · outbound

This paper cites Exponential improvements to the average- case hardness of bosonsampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Exponential improvements to the average- case hardness of bosonsampling

Reference 54

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source=pdf_text observed=2026-08-01T09:31:33.836496Z digest=sha256:b66d1d2ab1d271703255c6eee22b623fc30a461b0248685b7cda303fb7af6061

Observation 7d8359d0-802e-41ba-abfc-4d62e8a5a417 · outbound

This paper cites Characterizing quantum supremacy in near-term devices.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Characterizing quantum supremacy in near-term devices

Reference 55

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source=pdf_text observed=2026-08-01T09:31:33.856410Z digest=sha256:0bc9a0179f5f937b6c78b9e7e164f3061cb587f6930cabfa2da775f37e1e69d2

Observation 3730f49a-4e5e-4527-a04f-e11760ce91b4 · outbound

This paper cites Fourier analysis of sampling from noisy chaotic quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Fourier analysis of sampling from noisy chaotic quantum circuits

Reference 56

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source=pdf_text observed=2026-08-01T09:31:33.866305Z digest=sha256:8dfa080855ef323047904e285b375854c38af957052f72a5f514f3705d6e047a

Observation 88dc26ce-7872-433d-9aea-872aa42718b4 · outbound

This paper cites Effect of nonunital noise on random-circuit sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Effect of nonunital noise on random-circuit sampling

Reference 57

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source=pdf_text observed=2026-08-01T09:31:33.877736Z digest=sha256:6ac394f2bbe837196982ea8e60e43f386efc943fdd411cfc6ce96dd33efe5041

Observation 2508ea9c-38c5-4b31-b05e-819db9e7eec9 · outbound

This paper cites Entanglement dynamics of noisy random circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Entanglement dynamics of noisy random circuits

Reference 58

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source=pdf_text observed=2026-08-01T09:31:33.889215Z digest=sha256:50b2c10f5bd6f19cb3821ac6d231af87ab6bd69d327b8cd781ae2f33c13c6834

Observation 4027799e-b24c-44cb-965e-f5b34786ca56 · outbound

This paper cites Entanglement entropy scaling of noisy random quantum circuits in two dimensions.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Entanglement entropy scaling of noisy random quantum circuits in two dimensions

Reference 59

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source=pdf_text observed=2026-08-01T09:31:33.904136Z digest=sha256:98a0fccd64410321c613733e505220bd48f4a957ebf6bcf43ce8610e97641ead

Observation 834fd232-a7fa-448f-8bf2-a20da742ee99 · outbound

This paper cites Noise-induced entanglement transition in one-dimensional random quantum circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Noise-induced entanglement transition in one-dimensional random quantum circuits

Reference 60

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source=pdf_text observed=2026-08-01T09:31:33.919106Z digest=sha256:c9554cbcd9c1f81975a1126964e6812aec68d4dc46d7f43b0a6703c411443a57

Observation 23345062-8de2-465d-9e65-a10e62d1aef0 · outbound

This paper cites The computational complexity of linear optics.

Hardness and Complexity Transition of Noisy Random Circuit Sampling The computational complexity of linear optics

Reference 61

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source=pdf_text observed=2026-08-01T09:31:33.927725Z digest=sha256:25bd1c9e179ad71f1265a95047f4dafcfc088236a812a7f387c6a5cafcf478a1

Observation addff42e-bcfd-453e-ac66-141f49a21b86 · outbound

This paper cites Exploring shallow-depth boson sampling: Toward a scalable quantum advantage.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Exploring shallow-depth boson sampling: Toward a scalable quantum advantage

Reference 62

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source=pdf_text observed=2026-08-01T09:31:33.937881Z digest=sha256:97ccf18d033714e4e49ea20286888ffa12a53734ca74d574ca244c480d7f016e

Observation fbeb1702-78eb-48fc-b0c6-86c623edcd4a · outbound

This paper cites Complexity Classification of Conjugated Clifford Circuits.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Complexity Classification of Conjugated Clifford Circuits

Reference 63

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source=pdf_text observed=2026-08-01T09:31:33.950365Z digest=sha256:2f0a00292da7e47e52b3007dfc5a72e46779eb79e9b89afa2b03dbad0b9c78e8

Observation e5461e72-572e-4d2e-9c58-9cac4d8d6113 · outbound

This paper cites Quantum computational advantage of noisy boson sampling with partially distinguishable photons.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Quantum computational advantage of noisy boson sampling with partially distinguishable photons

Reference 64

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source=pdf_text observed=2026-08-01T09:31:33.973539Z digest=sha256:a9f418f0e8afc9e7704711847bc9bb648dd3e000f9593ef7938df0d3e3467972

Observation ede5357c-1959-4732-96ef-cfd9fa237ad6 · outbound

This paper cites Sufficient conditions for hardness of lossy gaussian boson sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Sufficient conditions for hardness of lossy gaussian boson sampling

Reference 65

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source=pdf_text observed=2026-08-01T09:31:33.983339Z digest=sha256:a5109ac4f3c0594373cbe388dbacf8a55ba2aaef500d1437f18bfe7f1816cfec

Observation 926ebc2d-46ec-4dec-bb66-35c91cedb037 · outbound

This paper cites Complexity-theoretic foundations of BosonSampling with a linear number of modes.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Complexity-theoretic foundations of BosonSampling with a linear number of modes

Reference 66

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source=pdf_text observed=2026-08-01T09:31:33.994732Z digest=sha256:66c6c83db543e5b38b15894079af3784c1bc08f6c3e583e492c6999584c2171c

Observation e99f9f77-0b40-4a44-b275-7be9ac663816 · outbound

This paper cites Pp is as hard as the polynomial-time hierarchy.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Pp is as hard as the polynomial-time hierarchy

Reference 67

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source=pdf_text observed=2026-08-01T09:31:34.008579Z digest=sha256:1fcd175d06211179993b16feb5f470c06b400146a240d8f769a0791f46b004b1

Observation 3d69818a-8b68-4e4a-ba07-2910de2b84cd · outbound

This paper cites Efficient classical algorithm for boson sampling with partially distinguishable photons.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient classical algorithm for boson sampling with partially distinguishable photons

Reference 68

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source=pdf_text observed=2026-08-01T09:31:34.014328Z digest=sha256:65b82b583f985a8c1313bf548123de95e0e4f79bf764d0776ca0546d430e0a3a

Observation cfb798b4-e373-432f-a029-4b06630e353c · outbound

This paper cites Classically simulating near- term partially-distinguishable and lossy boson sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classically simulating near- term partially-distinguishable and lossy boson sampling

Reference 69

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source=pdf_text observed=2026-08-01T09:31:34.019980Z digest=sha256:a8a90675153022ebf9d73ec18f8947bceb645c2d8ba13d5884485fca4cd3e98d

Observation 0114159b-cd31-41df-b7e6-d261d4e02b29 · outbound

This paper cites Noise in boson sampling and the threshold of efficient classical simulatability.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Noise in boson sampling and the threshold of efficient classical simulatability

Reference 70

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source=pdf_text observed=2026-08-01T09:31:34.026856Z digest=sha256:292cc3761fac62f1fa01aaa9366a7406f2ad3f2d567482fc1452947fc140d047

Observation 64bc52aa-3a1f-4987-9b80-822c1b30e3ce · outbound

This paper cites Simulating boson sampling in lossy architectures.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Simulating boson sampling in lossy architectures

Reference 71

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source=pdf_text observed=2026-08-01T09:31:34.043031Z digest=sha256:c36798bd3ced4206819db54dead5f428fec9df2979ee2416328f2623121b6da0

Observation e98d4d6d-28ce-406a-9189-e80ac1ebbe67 · outbound

This paper cites Classical simulation of photonic linear optics with lost particles.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulation of photonic linear optics with lost particles

Reference 72

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source=pdf_text observed=2026-08-01T09:31:34.052676Z digest=sha256:f61580a98fdbce540fd5a6da91722478ac69680341d773fd63b265004c803bca

Observation 02aeca3b-9035-4ba3-9dab-446ba4859552 · outbound

This paper cites Classical simulation of linear optics subject to nonuniform losses.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulation of linear optics subject to nonuniform losses

Reference 73

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source=pdf_text observed=2026-08-01T09:31:34.057351Z digest=sha256:71d7b8e24568923b8972f47c996ec044d697efc472001579324a989ec9aab8cc

Observation ce6deaac-4f13-4479-83d4-a84f1e7af082 · outbound

This paper cites Classical simulation of lossy boson sampling using matrix product operators.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulation of lossy boson sampling using matrix product operators

Reference 74

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source=pdf_text observed=2026-08-01T09:31:34.065025Z digest=sha256:7cd418acec29541c8dd34f07f8f3af4925677d5efe237520cf500b99cf59f0e9

Observation 96452bc7-951a-4678-b1d0-2510eedf8f36 · outbound

This paper cites On classical simulation algorithms for noisy Boson Sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling On classical simulation algorithms for noisy Boson Sampling

Reference 75

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source=pdf_text observed=2026-08-01T09:31:34.082928Z digest=sha256:29a3ee87f1f911464caf15b79245752439e28db0adb4614b5b51114691335fbe

Observation c0fdf15c-18a8-41b1-8098-e8b300a6e757 · outbound

This paper cites Classical simulability of constant- depth linear-optical circuits with noise.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulability of constant- depth linear-optical circuits with noise

Reference 76

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source=pdf_text observed=2026-08-01T09:31:34.090838Z digest=sha256:cdcfef294f855eca34093c15d961e798cffe75b927c1840ffee72595e06f8f5d

Observation bdd32dfe-f8e7-455d-8883-d4084fd599d8 · outbound

This paper cites Achieving quantum supremacy with sparse and noisy commuting quantum computations.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Achieving quantum supremacy with sparse and noisy commuting quantum computations

Reference 77

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source=pdf_text observed=2026-08-01T09:31:34.099362Z digest=sha256:e95b213c13d1573c8f7aeebc91716a33a7058fd548f1a12eb3f94baf374c8bd1

Observation 752f14c0-47a0-4211-afe6-118f8347fb36 · outbound

This paper cites Polynomial-time classical simulation of noisy iqp circuits with constant depth.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Polynomial-time classical simulation of noisy iqp circuits with constant depth

Reference 78

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source=pdf_text observed=2026-08-01T09:31:34.121199Z digest=sha256:7011ffb14e1c9bb34ac70dfc7af03ecc3e9da0afdd2ac5458eb35f4e94586ab1

Observation c02887bb-e6a4-414e-86ff-2d8af4b7c979 · outbound

This paper cites Recent theoretical and experimental progress on boson sampling.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Recent theoretical and experimental progress on boson sampling

Reference 79

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source=pdf_text observed=2026-08-01T09:31:34.130750Z digest=sha256:e89bf2d7d0348dc6b430cfd8ac86ed6c9bd05a8658dee7fd3ffd9019271e39db

Observation 29322568-ff2f-42a6-81f3-a0c2a3786fbd · outbound

This paper cites Faster algorithms via approximation theory.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Faster algorithms via approximation theory

Reference 80

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Observation 2d1d410a-71bb-4c64-a47b-0f883ddd5ae0 · outbound

This paper cites Chebyshev polynomials.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Chebyshev polynomials

Reference 81

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Observation 2353a02c-765e-4a80-bd4b-d868f93bf993 · outbound

This paper cites Le¸ cons sur les fonctions de variables r´ eelles et les d´ eveloppements en s´ eries de polynˆ omes.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Le¸ cons sur les fonctions de variables r´ eelles et les d´ eveloppements en s´ eries de polynˆ omes

Reference 82

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Observation 62f98c39-7946-4317-9e9a-0c7d9dc6e5f1 · outbound

This paper cites Approximation theory and approximation practice, extended edition.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Approximation theory and approximation practice, extended edition

Reference 83

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Observation c1ca1cd4-4430-45f1-8a15-b87c5c29e731 · outbound

This paper cites A survey of practical rational and polynomial approximation of functions.

Hardness and Complexity Transition of Noisy Random Circuit Sampling A survey of practical rational and polynomial approximation of functions

Reference 84

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Observation 8b2bd48e-1299-40ed-b0b5-2e5ca9a7c278 · outbound

This paper cites Chebyshev series expansion of inverse polynomials.

Hardness and Complexity Transition of Noisy Random Circuit Sampling Chebyshev series expansion of inverse polynomials

Reference 85

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