Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-01T09:31:34.189845Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-01T09:31:34.189845Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
85 of 85 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation ec7a1c23-597b-4c9a-bec6-9f01d985a160 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Subsequently, Ref
Reference 1
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Observation 0c84b758-8f2d-41d8-95cb-8ec723d8a436 · outbound
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
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
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
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
Hardness and Complexity Transition of Noisy Random Circuit Sampling ( 10), respectively
Reference 6
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Observation 415e57dc-4ee2-4319-99ba-e2e62976ccb3 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling simulation
Reference 7
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Observation 4d9d0261-851e-4063-ac21-63dfbfe9e685 · outbound
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
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
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
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
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
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
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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Observation 8ec9d64d-288f-4990-85cd-dce4f87b2ee5 · outbound
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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Observation bfab0a63-2dc6-4f8c-99da-c1cf2a1bff77 · outbound
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
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
Hardness and Complexity Transition of Noisy Random Circuit Sampling A polynomial-time classical algorithm for noisy quantum circuits
Reference 37
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Observation f9bd99d8-9871-4387-be7e-1b47c434f92e · outbound
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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Observation 30f49c3a-cbe5-45ff-8704-7fad17e66bff · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulations 20 of noisy variational quantum circuits
Reference 39
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Observation 3e814de6-4813-4fd3-a02f-d421863aab43 · outbound
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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Observation f0327402-017f-4e3c-bcf2-c51a901ea2ca · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Simulating noisy quantum circuits with matrix product density operators
Reference 41
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Observation 000ec9b0-e274-4582-9e0c-8084df9b6117 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Unresolved cited work
Reference 42
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Observation fcbd34d2-b609-47ec-b172-d9bbc9ff59c3 · outbound
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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Observation 793ce953-b17e-4d8d-be31-6b8ae194123a · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Relative entropy convergence for depolarizing channels
Reference 44
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Observation 4a76f173-c592-436d-aa96-57bb337fa20a · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Noise-induced shallow circuits and absence of barren plateaus
Reference 45
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Observation 19985060-b80b-45fe-90f5-9a1cf3221213 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Limitations of optimization algorithms on noisy quantum devices
Reference 46
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Observation 7147ef85-f91d-411d-9592-503e47541cc4 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient classical simulation of random shallow 2d quantum circuits
Reference 47
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Observation 85989711-1d34-468a-9399-bba9fbab96f4 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient sampling of noisy shallow circuits via monitored unraveling
Reference 48
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Observation c0c6b4be-9771-4616-81c2-5bc0f8bdd391 · outbound
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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Observation 188b53da-98d7-479a-bb0d-38391c544ead · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Efficient simulation of one-dimensional quantum many-body systems
Reference 50
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Observation bd44780c-10fb-40c5-8ac7-0f96e21826aa · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Simulating quantum computation by contracting tensor networks
Reference 51
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Observation c97059cc-63ef-4bec-a1f3-cc2584355e99 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling On the simulation of quantum circuits
Reference 52
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Observation 320fff38-51b5-4b81-8e47-755498e2e697 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling On approximation algorithms for# p
Reference 53
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Observation eaf086b4-a4a0-4f3f-b0ce-fe6185bad682 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Exponential improvements to the average- case hardness of bosonsampling
Reference 54
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Observation 7d8359d0-802e-41ba-abfc-4d62e8a5a417 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Characterizing quantum supremacy in near-term devices
Reference 55
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Observation 3730f49a-4e5e-4527-a04f-e11760ce91b4 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Fourier analysis of sampling from noisy chaotic quantum circuits
Reference 56
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Observation 88dc26ce-7872-433d-9aea-872aa42718b4 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Effect of nonunital noise on random-circuit sampling
Reference 57
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Observation 2508ea9c-38c5-4b31-b05e-819db9e7eec9 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Entanglement dynamics of noisy random circuits
Reference 58
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Observation 4027799e-b24c-44cb-965e-f5b34786ca56 · outbound
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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Observation 834fd232-a7fa-448f-8bf2-a20da742ee99 · outbound
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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Observation 23345062-8de2-465d-9e65-a10e62d1aef0 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling The computational complexity of linear optics
Reference 61
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Observation addff42e-bcfd-453e-ac66-141f49a21b86 · outbound
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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Observation fbeb1702-78eb-48fc-b0c6-86c623edcd4a · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Complexity Classification of Conjugated Clifford Circuits
Reference 63
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Observation e5461e72-572e-4d2e-9c58-9cac4d8d6113 · outbound
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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Observation ede5357c-1959-4732-96ef-cfd9fa237ad6 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Sufficient conditions for hardness of lossy gaussian boson sampling
Reference 65
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Observation 926ebc2d-46ec-4dec-bb66-35c91cedb037 · outbound
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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Observation e99f9f77-0b40-4a44-b275-7be9ac663816 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Pp is as hard as the polynomial-time hierarchy
Reference 67
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Observation 3d69818a-8b68-4e4a-ba07-2910de2b84cd · outbound
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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Observation cfb798b4-e373-432f-a029-4b06630e353c · outbound
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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Observation 0114159b-cd31-41df-b7e6-d261d4e02b29 · outbound
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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Observation 64bc52aa-3a1f-4987-9b80-822c1b30e3ce · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Simulating boson sampling in lossy architectures
Reference 71
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Observation e98d4d6d-28ce-406a-9189-e80ac1ebbe67 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulation of photonic linear optics with lost particles
Reference 72
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Observation 02aeca3b-9035-4ba3-9dab-446ba4859552 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Classical simulation of linear optics subject to nonuniform losses
Reference 73
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Observation ce6deaac-4f13-4479-83d4-a84f1e7af082 · outbound
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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Observation 96452bc7-951a-4678-b1d0-2510eedf8f36 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling On classical simulation algorithms for noisy Boson Sampling
Reference 75
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Observation c0fdf15c-18a8-41b1-8098-e8b300a6e757 · outbound
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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Observation bdd32dfe-f8e7-455d-8883-d4084fd599d8 · outbound
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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Observation 752f14c0-47a0-4211-afe6-118f8347fb36 · outbound
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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Observation c02887bb-e6a4-414e-86ff-2d8af4b7c979 · outbound
Hardness and Complexity Transition of Noisy Random Circuit Sampling Recent theoretical and experimental progress on boson sampling
Reference 79
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Observation 29322568-ff2f-42a6-81f3-a0c2a3786fbd · outbound
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
Hardness and Complexity Transition of Noisy Random Circuit Sampling Chebyshev polynomials
Reference 81
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Observation 2353a02c-765e-4a80-bd4b-d868f93bf993 · outbound
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
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
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
Hardness and Complexity Transition of Noisy Random Circuit Sampling Chebyshev series expansion of inverse polynomials
Reference 85
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