Paper Citation Record · LEDGER

Generative quantum advantage for classical and quantum problems

As of 10 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 13 inbound Pith citation observations for arXiv:2509.09033.

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

pith.paper-citation-record.v1
2509.09033 v1

Coverage vector

measured 46 of 46 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-04T19:55:13.495615Z

measured 59 of 59 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 13 of 13 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T01:33:05.230724Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T15:25:48.683365Z

Reference resolution

46 of 46 outbound references displayed

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External citation measurements

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Outbound references

Observation 33850dc5-d3ff-44ee-8e40-2ed453777ec5 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 1

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Observation ab0ad83b-1c02-4e69-a8d8-12a097df54f9 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 2

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Observation 6f9a425a-82b1-4a91-87f3-026f64c96875 · outbound

This paper cites The measurement collapses the state to a product state|𝜑ℓ⟩= ⨂︀𝑛 𝑖=1|𝜑ℓ,𝑖⟩.

Generative quantum advantage for classical and quantum problems The measurement collapses the state to a product state|𝜑ℓ⟩= ⨂︀𝑛 𝑖=1|𝜑ℓ,𝑖⟩

Reference 3

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Observation 5cdc4e2b-6232-497b-9062-072d7be4df61 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 4

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Observation e5eba01c-f1d6-4d4e-99c1-75ac8f188b23 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 5

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Observation c4b2c791-ef30-4c3f-84e6-f0cfd149d317 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 6

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Observation db267170-aa0c-42db-84c0-aff66d7babac · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 7

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Observation 5b27a739-28f3-4431-8e10-e744f73d82b8 · outbound

This paper cites barren plateau problem.

Generative quantum advantage for classical and quantum problems barren plateau problem

Reference 8

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Observation 6886461b-2241-40c1-a0e6-5a83f8e50fc2 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 9

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Observation 85d6e3f7-a8ea-44a8-a472-bdee90b245a4 · outbound

This paper cites Proof.These properties follow directly from strong convexity: strictly convex functions have a unique global mini- mizer, and any stationary point must be this minimum.

Generative quantum advantage for classical and quantum problems Proof.These properties follow directly from strong convexity: strictly convex functions have a unique global mini- mizer, and any stationary point must be this minimum

Reference 10

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Observation 54265a13-7877-4541-b4a3-dff2ec8a05d2 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 11

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Observation a3a3f644-387b-4ac2-b995-77cdf49d05ea · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 12

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Observation a2755591-bd12-4071-9cae-c7b82958c285 · outbound

This paper cites The QNN generates an𝑚-bit string𝑦∈{0,1} 𝑚 according to a distribution𝑝QNN(𝑦|𝑥; ⃗𝜃)that depends on the input bitstring𝑥∈{0,1} 𝑛 and the trainable circuit parameters⃗𝜃.

Generative quantum advantage for classical and quantum problems The QNN generates an𝑚-bit string𝑦∈{0,1} 𝑚 according to a distribution𝑝QNN(𝑦|𝑥; ⃗𝜃)that depends on the input bitstring𝑥∈{0,1} 𝑛 and the trainable circuit parameters⃗𝜃

Reference 13

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Observation f159ee7c-5714-447b-9e12-fac8542012cb · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 14

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Observation f39cac8f-438b-4212-b4c4-8a3145c43c46 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 15

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Observation eadf3c41-6bdb-4aee-9da6-30ea19f3df20 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 16

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Observation 1e46db79-bbe6-4819-89ca-463862dfa240 · outbound

This paper cites This quantum circuit is shallow with𝒪(1)circuit depth regardless of the number of qubits.

Generative quantum advantage for classical and quantum problems This quantum circuit is shallow with𝒪(1)circuit depth regardless of the number of qubits

Reference 17

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Observation bff5b07d-76f9-4408-85be-888e83bd1cd2 · outbound

This paper cites ·𝑛𝐷)-qubit state|𝜑⟩to be the product state given by𝑥restricted to the coordinates (1, 𝑖2,.

Generative quantum advantage for classical and quantum problems ·𝑛𝐷)-qubit state|𝜑⟩to be the product state given by𝑥restricted to the coordinates (1, 𝑖2,

Reference 18

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Observation 01a105e3-cd30-488e-b00d-564376cc5d75 · outbound

This paper cites This parameter indexes both the first coordinate of the shallow quantum circuit and the circuit layer of the corresponding deep quantum circuit.

Generative quantum advantage for classical and quantum problems This parameter indexes both the first coordinate of the shallow quantum circuit and the circuit layer of the corresponding deep quantum circuit

Reference 19

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Observation 6de8f7dc-499f-463b-b1a5-74d8cb6cf42b · outbound

This paper cites , 𝑖𝐷)with rotation angles𝜃(𝑖1,𝑖2,...,𝑖𝐷) determined by the QNN, for all𝑖2,.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)with rotation angles𝜃(𝑖1,𝑖2,...,𝑖𝐷) determined by the QNN, for all𝑖2,

Reference 20

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Observation 0fa6da35-3afd-499f-a1f2-1a96ab40a743 · outbound

This paper cites , 𝑖𝐷)and(𝑖 1, 𝑖′ 2,.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)and(𝑖 1, 𝑖′ 2,

Reference 21

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Observation 8725b265-dbb8-4dd3-a7f8-85f330297eba · outbound

This paper cites , 𝑖𝐷)for all𝑖 2,.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)for all𝑖 2,

Reference 22

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Observation 4db672f6-c8d6-4e94-89dd-c02af810df86 · outbound

This paper cites , 𝑖𝐷)for all𝑖 2,.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)for all𝑖 2,

Reference 23

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Observation 44411cf1-b5ee-4427-9c8a-a9a07565936a · outbound

This paper cites , 𝑖𝐷)is a component of|𝜑 (𝑖1)⟩, |𝜑(𝑖1)⟩=|0⟩⊗| ̃︀𝜑(𝑖1) 0 ⟩+|1⟩⊗| ̃︀𝜑(𝑖1) 1 ⟩,(S.2.2) for some unnormalized states|̃︀𝜑(𝑖1) 0 ⟩,| ̃︀𝜑(𝑖1) 1 ⟩.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)is a component of|𝜑 (𝑖1)⟩, |𝜑(𝑖1)⟩=|0⟩⊗| ̃︀𝜑(𝑖1) 0 ⟩+|1⟩⊗| ̃︀𝜑(𝑖1) 1 ⟩,(S.2.2) for some unnormalized states|̃︀𝜑(𝑖1) 0 ⟩,| ̃︀𝜑(𝑖1) 1 ⟩

Reference 24

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Observation 1e3797b0-a799-43b4-9b95-245729c91513 · outbound

This paper cites , 𝑖𝐷)is initialized to|+⟩= 1√ 2(|0⟩+|1⟩)as specified by the condition on the input bit𝑥(𝑖1+1,𝑖2,...,𝑖𝐷) = 0.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)is initialized to|+⟩= 1√ 2(|0⟩+|1⟩)as specified by the condition on the input bit𝑥(𝑖1+1,𝑖2,...,𝑖𝐷) = 0

Reference 25

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Observation 3b7c433d-343c-4c35-bf1d-2476d8f07374 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 26

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Observation b681a1ec-5a2a-44db-afe8-0e80a17a60c0 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

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Observation 8b894cd8-1bb0-4bb5-8066-86b8ad5fb3a0 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 28

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Observation 8d1379e6-e79c-4b55-a8a9-bb6da0debcc9 · outbound

This paper cites , 𝑖𝐷)-th qubit of|𝜑⟩if𝑦 (𝑖1,𝑖2,...,𝑖𝐷) = 1maps the state to|0⟩⊗ | ̃︀𝜑(𝑖1) 0 ⟩+|1⟩⊗| ̃︀𝜑(𝑖1) 1 ⟩=|𝜑 (𝑖1)⟩in both cases of𝑦 (𝑖1,𝑖2,...,𝑖𝐷).

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)-th qubit of|𝜑⟩if𝑦 (𝑖1,𝑖2,...,𝑖𝐷) = 1maps the state to|0⟩⊗ | ̃︀𝜑(𝑖1) 0 ⟩+|1⟩⊗| ̃︀𝜑(𝑖1) 1 ⟩=|𝜑 (𝑖1)⟩in both cases of𝑦 (𝑖1,𝑖2,...,𝑖𝐷)

Reference 29

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Observation 4ee854c6-f622-480f-84a3-4064b2aee6c9 · outbound

This paper cites , 𝑖𝐷)is initialized to|0⟩.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)is initialized to|0⟩

Reference 30

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Observation a56fd203-8caa-45a7-9dc8-b51fd2c50264 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 31

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Observation 7a483256-eea9-4240-8e8b-cadf0109e9b4 · outbound

This paper cites , 𝑖𝐷)in the𝑋basis is equivalent to measuring the qubit at position(𝑖 2,.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)in the𝑋basis is equivalent to measuring the qubit at position(𝑖 2,

Reference 32

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Observation 463d686a-3890-4bef-a6b4-66f36a41e626 · outbound

This paper cites , 𝑖𝐷)in the state|𝜑 (𝑖1)⟩to|0⟩.

Generative quantum advantage for classical and quantum problems , 𝑖𝐷)in the state|𝜑 (𝑖1)⟩to|0⟩

Reference 33

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Observation baa54f1d-476a-49d7-b405-ef6122b8f160 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

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Observation 8ff473b9-8dd1-43d3-8e6b-305136bcc7e3 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 35

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Observation 7c32ac99-57e9-43a8-aedf-c5e39b782a2d · outbound

This paper cites 45 By induction, after all𝑛1 layers, the final state|𝜑(𝑛1)⟩is the same as the state after all𝑛1 layers of the deep QNN.

Generative quantum advantage for classical and quantum problems 45 By induction, after all𝑛1 layers, the final state|𝜑(𝑛1)⟩is the same as the state after all𝑛1 layers of the deep QNN

Reference 36

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Observation ba083d06-4321-41fd-a1cc-3792e7206ff3 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 37

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Observation 1c855eb3-e727-4fdd-92a2-3dcc155edd9e · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 38

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Observation 70a24c0c-d9fd-4973-a3e0-d631e9e18718 · outbound

This paper cites We now define the family of deep quantum circuits, which corresponds to injecting different patterns of single- qubit𝑍gates in each round of the circuit layers.

Generative quantum advantage for classical and quantum problems We now define the family of deep quantum circuits, which corresponds to injecting different patterns of single- qubit𝑍gates in each round of the circuit layers

Reference 39

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Observation 9e749b2b-cb07-470d-a769-9b11a6deee15 · outbound

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Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 40

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Observation 2133bcbe-fc9f-4952-b8ab-513b33791330 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 41

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Observation 895fa443-4fca-4b6f-9aaa-ff825f877b43 · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 42

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Observation efbb5d81-7e51-4179-97b4-3510eeb9886c · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 43

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Observation a3f6b516-f63d-4565-b09a-ac492d72c79d · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 44

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Observation 8c17b8f9-3418-4f8c-b4dd-5c68fac4c3ef · outbound

This paper cites an unresolved cited work.

Generative quantum advantage for classical and quantum problems Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-04T19:55:13.490123Z

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Observation 61aebb79-7d4b-42f5-9124-4805660c2c79 · outbound

This paper cites This quantum circuit is shallow with𝒪(1)circuit depth regardless of the number of qubits.

Generative quantum advantage for classical and quantum problems This quantum circuit is shallow with𝒪(1)circuit depth regardless of the number of qubits

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-04T19:55:13.495615Z

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Pith citing papers

Observation 6f88a7b7-5b3f-4fb7-b817-77fb7a95b0e0 · inbound

Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation cites this paper.

Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation Generative quantum advantage for classical and quantum problems

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T20:03:56.914012Z

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Observation 2cc8b62c-24d1-4f6a-88d7-19ba3cffcae4 · inbound

Toward Generative Quantum Utility via Correlation-Complexity Map cites this paper.

Toward Generative Quantum Utility via Correlation-Complexity Map Generative quantum advantage for classical and quantum problems

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-15T15:06:09.799486Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b82d8f48-c44c-429d-809f-9a0270309154 · inbound

Spectral methods: crucial for machine learning, natural for quantum computers? cites this paper.

Spectral methods: crucial for machine learning, natural for quantum computers? Generative quantum advantage for classical and quantum problems

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-15T00:23:22.301165Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 21ee4277-ba0c-40f6-9683-27ea98f6ba54 · inbound

Exponential quantum advantage in processing massive classical data cites this paper.

Exponential quantum advantage in processing massive classical data Generative quantum advantage for classical and quantum problems

Reference 28

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T07:26:00.212876Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7206dce5-9a13-47fb-bd83-90d0c2be3eb5 · inbound

Minimizing classical resources in variational measurement-based quantum computation for generative modeling cites this paper.

Minimizing classical resources in variational measurement-based quantum computation for generative modeling Generative quantum advantage for classical and quantum problems

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-11T09:41:02.429198Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f39e7f0c-5b49-4fe0-9f24-5c5be6b90b5b · inbound

Quantum computation at the edge of chaos cites this paper.

Quantum computation at the edge of chaos Generative quantum advantage for classical and quantum problems

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-05-10T10:44:37.561291Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3ff8c969-8b69-48dd-85fe-ec597f7ab1dc · inbound

Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms cites this paper.

Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms Generative quantum advantage for classical and quantum problems

Reference 21

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T11:01:30.333018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 984a68ad-a711-4779-b51e-e4fb9be4f0a8 · inbound

Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning cites this paper.

Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning Generative quantum advantage for classical and quantum problems

Reference 43

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T04:00:56.375108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9daea9a7-845e-48f7-99ed-5b286a157316 · inbound

Software Between Quantum and Machine Learning -- And Down to Pulses cites this paper.

Software Between Quantum and Machine Learning -- And Down to Pulses Generative quantum advantage for classical and quantum problems

Reference 7

Resolution: malformed identifier; arxiv_id, observed 2026-05-21T04:34:34.446769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6538e2c2-1271-4f97-bcdf-8b14a59ea532 · inbound

Software Between Quantum and Machine Learning -- And Down to Pulses cites this paper.

Software Between Quantum and Machine Learning -- And Down to Pulses Generative quantum advantage for classical and quantum problems

Reference 7

Resolution: malformed identifier; arxiv_id, observed 2026-07-01T15:05:48.469496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ccd04b27-c16c-494e-9ce4-e9162b3da90c · inbound

Quantum Fourier Generative Models Trainable at Large Scale cites this paper.

Quantum Fourier Generative Models Trainable at Large Scale Generative quantum advantage for classical and quantum problems

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-07-01T15:25:48.685455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8eb6862d-5715-481a-aa90-9a8331357348 · inbound

Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis cites this paper.

Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis Generative quantum advantage for classical and quantum problems

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-06-30T07:04:21.187955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 21ac2674-2a41-49b7-9862-969431a638d7 · inbound

Generative IQP Circuit Learning with Physics-Informed Latent Initialization cites this paper.

Generative IQP Circuit Learning with Physics-Informed Latent Initialization Generative quantum advantage for classical and quantum problems

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T01:33:05.230724Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.