Trainability and Mode Separation of Mixed IQP-QCBMs | Paper Citation Record

Observation 9a036648-953b-4552-b3d9-6686ef3c572b · outbound

This paper cites Benedetti, D.

Trainability and Mode Separation of Mixed IQP-QCBMs Benedetti, D

Reference 1

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Observation a22c80e4-3b4e-4130-8283-c3a0cec86218 · outbound

This paper cites Liu and L.

Trainability and Mode Separation of Mixed IQP-QCBMs Liu and L

Reference 2

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Observation 305b74ea-3473-43e2-85c1-47784e902631 · outbound

This paper cites Coyle, D.

Trainability and Mode Separation of Mixed IQP-QCBMs Coyle, D

Reference 3

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Observation bb5a5e90-8af9-4936-843a-6326b0cdd0a9 · outbound

This paper cites Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy.

Trainability and Mode Separation of Mixed IQP-QCBMs Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

Reference 4

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Observation 0e5b7f9b-2466-4ada-93c7-4cd3c901f52d · outbound

This paper cites Power of Quantum Generative Learning.

Trainability and Mode Separation of Mixed IQP-QCBMs Power of Quantum Generative Learning

Reference 5

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Observation b20c1e1d-b945-45ad-b888-c8ff129d8da8 · outbound

This paper cites Cerezo, A.

Trainability and Mode Separation of Mixed IQP-QCBMs Cerezo, A

Reference 7

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Observation 97d8da04-c0e1-40d7-83b6-a8ebcfe15403 · outbound

This paper cites Van den Nest, Simulating quantum computers with probabilistic methods, Quantum Information and Com- putation11, 784 (2011).

Trainability and Mode Separation of Mixed IQP-QCBMs Van den Nest, Simulating quantum computers with probabilistic methods, Quantum Information and Com- putation11, 784 (2011)

Reference 8

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Observation e793ac17-d013-488b-8e26-292dfc686624 · outbound

This paper cites Recio-Armengol, S.

Trainability and Mode Separation of Mixed IQP-QCBMs Recio-Armengol, S

Reference 9

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Reference 12

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Observation 67ed6eae-c1e4-432c-bd58-9a2ed326ace8 · outbound

This paper cites Lerch, J.

Trainability and Mode Separation of Mixed IQP-QCBMs Lerch, J

Reference 13

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Observation d1a79a35-c4fa-4f15-9281-6c132c90bae0 · outbound

This paper cites Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization.

Trainability and Mode Separation of Mixed IQP-QCBMs Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization

Reference 15

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Observation 7e095544-ee26-44e7-87d8-cb3c5ea0fc4f · outbound

This paper cites Kurkin, K.

Trainability and Mode Separation of Mixed IQP-QCBMs Kurkin, K

Reference 16

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Observation 69e8918a-6faa-4808-87d1-ad60009036ca · outbound

This paper cites Note on the Universality of Parameterized IQP Circuits with Hidden Units for Generating Probability Distributions.

Trainability and Mode Separation of Mixed IQP-QCBMs Note on the Universality of Parameterized IQP Circuits with Hidden Units for Generating Probability Distributions

Reference 17

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Observation b4722961-895e-4923-ab88-8f3d2daea4e0 · outbound

This paper cites Zhong, X.

Trainability and Mode Separation of Mixed IQP-QCBMs Zhong, X

Reference 18

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Observation f7b9dc00-89d4-438f-9ea1-1e426083fa80 · outbound

This paper cites Generative training of quantum Boltzmann machines with hidden units.

Trainability and Mode Separation of Mixed IQP-QCBMs Generative training of quantum Boltzmann machines with hidden units

Reference 19

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Observation 47caa732-7e66-4223-807d-f183565cba83 · outbound

This paper cites An IQP Born Machine for Calorimeter Image Generation at 64 Qubits with Compiled-IQP Deployment.

Trainability and Mode Separation of Mixed IQP-QCBMs An IQP Born Machine for Calorimeter Image Generation at 64 Qubits with Compiled-IQP Deployment

Reference 20

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Observation b474af8b-bd81-4867-b3d0-212e0cb6b1e4 · outbound

This paper cites Cheng, J.

Trainability and Mode Separation of Mixed IQP-QCBMs Cheng, J

Reference 21

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Trainability and Mode Separation of Mixed IQP-QCBMs Unresolved cited work

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Observation 7d8dbda0-e6a7-4640-9d28-538215d51d06 · outbound

This paper cites Shepherd and M.

Trainability and Mode Separation of Mixed IQP-QCBMs Shepherd and M

Reference 23

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Observation bc6bba29-36e3-483e-a71e-c9050c7b83a6 · outbound

This paper cites Gretton, K.

Trainability and Mode Separation of Mixed IQP-QCBMs Gretton, K

Reference 24

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Observation aedd243a-46e6-468e-aa59-1a3285adcb6c · outbound

This paper cites Muandet, K.

Trainability and Mode Separation of Mixed IQP-QCBMs Muandet, K

Reference 25

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Observation 804e2a66-4f9b-4849-8661-f2d3898b11c8 · outbound

This paper cites Li, W.-C.

Trainability and Mode Separation of Mixed IQP-QCBMs Li, W.-C

Reference 27

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Trainability and Mode Separation of Mixed IQP-QCBMs Unresolved cited work

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Observation 9ca7ffbf-b19d-4acf-ae1c-a703ca5ada91 · outbound

This paper cites Grant, L.

Trainability and Mode Separation of Mixed IQP-QCBMs Grant, L

Reference 29

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Observation eee3da0e-bcf9-458f-92ec-f65276b4bc9a · outbound

This paper cites Zhang, L.

Trainability and Mode Separation of Mixed IQP-QCBMs Zhang, L

Reference 30

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Observation 25c1661b-9812-4378-ac88-73c90673eb78 · outbound

This paper cites Learning to learn with quantum neural networks via classical neural networks.

Trainability and Mode Separation of Mixed IQP-QCBMs Learning to learn with quantum neural networks via classical neural networks

Reference 31

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Trainability and Mode Separation of Mixed IQP-QCBMs Unresolved cited work

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Observation 70bcccde-7eac-435b-953f-1ab42474a9af · outbound

This paper cites von Luxburg, A tutorial on spectral clustering, Statis- tics and Computing17, 395 (2007).

Trainability and Mode Separation of Mixed IQP-QCBMs von Luxburg, A tutorial on spectral clustering, Statis- tics and Computing17, 395 (2007)

Reference 33

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Observation 246e82b8-d35c-4007-bc0b-65e1aa47d8c8 · outbound

This paper cites Arrasmith, Z.

Trainability and Mode Separation of Mixed IQP-QCBMs Arrasmith, Z

Reference 34

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Observation 0ea2f55b-3000-4b0c-a599-24909a1f2dc7 · outbound

This paper cites Ghosh, V.

Trainability and Mode Separation of Mixed IQP-QCBMs Ghosh, V

Reference 35

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Observation 16fc6f45-7927-41b9-b2f3-dbb13e902845 · outbound

This paper cites Lecun, L.

Trainability and Mode Separation of Mixed IQP-QCBMs Lecun, L

Reference 36

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Observation 5bee1ce3-cb3a-478a-824c-497f5c6acdfe · outbound

This paper cites IQPopt: Fast optimization of instantaneous quantum polynomial circuits in JAX.

Trainability and Mode Separation of Mixed IQP-QCBMs IQPopt: Fast optimization of instantaneous quantum polynomial circuits in JAX

Reference 38

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Observation 6e6acb7a-38d3-44ac-81e9-8fe95df2d711 · outbound

This paper cites The Inductive Bias of Quantum Kernels.

Trainability and Mode Separation of Mixed IQP-QCBMs The Inductive Bias of Quantum Kernels

Reference 39

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Observation c347877d-f652-4950-8afa-122a232ec0a3 · outbound

This paper cites Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer.

Trainability and Mode Separation of Mixed IQP-QCBMs Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer

Reference 40

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Observation 0475c95a-560c-4a0c-91e6-b467991eb08b · outbound

This paper cites Spectral Born machines: classically trainable quantum generative models for discrete data.

Trainability and Mode Separation of Mixed IQP-QCBMs Spectral Born machines: classically trainable quantum generative models for discrete data

Reference 41

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Observation 18341079-1d51-4808-85cb-9e45189f005a · outbound

This paper cites Fast classical simulation of Harvard/QuEra IQP circuits.

Trainability and Mode Separation of Mixed IQP-QCBMs Fast classical simulation of Harvard/QuEra IQP circuits

Reference 42

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Observation 1b505902-a620-4bf5-a112-a64260721450 · outbound

This paper cites Scriva, E.

Trainability and Mode Separation of Mixed IQP-QCBMs Scriva, E

Reference 43

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Observation a9310d86-2115-4587-9f0d-f27bd41bf37c · outbound

This paper cites Demidik, C.

Trainability and Mode Separation of Mixed IQP-QCBMs Demidik, C

Reference 44

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Observation 88b674b9-0fa5-43db-b4ec-21553403fbb3 · outbound

This paper cites [8] in the main text.

Trainability and Mode Separation of Mixed IQP-QCBMs [8] in the main text

Reference 47

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Observation 76f5a69e-fc02-4526-94f1-2d8b25348a10 · outbound

This paper cites (12), so that one IQP-form circuit estimates the uniform mixture correlatorz A(Θ).

Trainability and Mode Separation of Mixed IQP-QCBMs (12), so that one IQP-form circuit estimates the uniform mixture correlatorz A(Θ)

Reference 48

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Observation 21b9138c-7c2a-4507-8356-66d35f24b1c0 · outbound

This paper cites It fixes the branch weights and proves the estimator equivalence.

Trainability and Mode Separation of Mixed IQP-QCBMs It fixes the branch weights and proves the estimator equivalence

Reference 49

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Trainability and Mode Separation of Mixed IQP-QCBMs Unresolved cited work

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Observation f4575f9a-a058-4d81-8b7f-bb1ddad8dfc8 · outbound

This paper cites Theπ ℓ weighting enters exactly once, in step 3; the allocation of step 1 only distributes the budget and applies no second weighting.

Trainability and Mode Separation of Mixed IQP-QCBMs Theπ ℓ weighting enters exactly once, in step 3; the allocation of step 1 only distributes the budget and applies no second weighting

Reference 52

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Observation d78be367-4b86-4896-af54-48a4ccf3f3c0 · outbound

This paper cites (A21) (Appendix A 3), each branch correlator obeysz A(θ(ℓ))∈[−1,1] as the expectation of a±1-eigenvalue Pauli word, andw A = Θ(n−|A|) is the low-body weight atσ= Θ( √n).

Trainability and Mode Separation of Mixed IQP-QCBMs (A21) (Appendix A 3), each branch correlator obeysz A(θ(ℓ))∈[−1,1] as the expectation of a±1-eigenvalue Pauli word, andw A = Θ(n−|A|) is the low-body weight atσ= Θ( √n)

Reference 53

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Observation 4f01c33f-57ce-4411-b26d-eda426e4947c · outbound

This paper cites Its curvature- to-variance step is Theorem 2 of Ref.

Trainability and Mode Separation of Mixed IQP-QCBMs Its curvature- to-variance step is Theorem 2 of Ref

Reference 54

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Observation b709e99e-25e9-42b4-9956-273e951574d2 · outbound

This paper cites We evaluate the curvature Eq.

Trainability and Mode Separation of Mixed IQP-QCBMs We evaluate the curvature Eq

Reference 55

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Observation 02df4d87-c470-43f5-8788-edbad58d106b · outbound

This paper cites III C and feeds it to the Master Lemma 1 to obtain the data-dependent counterpart of Theorem 1.

Trainability and Mode Separation of Mixed IQP-QCBMs III C and feeds it to the Master Lemma 1 to obtain the data-dependent counterpart of Theorem 1

Reference 56

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Observation bbeae8a9-0fe6-4ee4-8e19-b41dc6d86500 · outbound

This paper cites Its body-order-rescaled finite-size constant is Ck,eff :=nϵ 2/k k , q k,eff :=C k,eff /n.(B32) We compute the same quantities from the 95th percentile to expose the tail.

Trainability and Mode Separation of Mixed IQP-QCBMs Its body-order-rescaled finite-size constant is Ck,eff :=nϵ 2/k k , q k,eff :=C k,eff /n.(B32) We compute the same quantities from the 95th percentile to expose the tail

Reference 57

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Observation 8e4f247b-b81f-4e74-9d96-4d9d5cbe8b7b · outbound

This paper cites II C) that an ancilla-free IQP circuit is not universal [16]; we give a constructive version through the mixture.

Trainability and Mode Separation of Mixed IQP-QCBMs II C) that an ancilla-free IQP circuit is not universal [16]; we give a constructive version through the mixture

Reference 58

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Observation 8c527900-1a17-4c56-9acd-008f4c9fe073 · outbound

This paper cites II E 1 is branch-coincident, and a mixture whose branches coincide reduces to a single ancilla-free circuit.

Trainability and Mode Separation of Mixed IQP-QCBMs II E 1 is branch-coincident, and a mixture whose branches coincide reduces to a single ancilla-free circuit

Reference 59

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This paper cites The MNIST data-agnostic runs are listed separately because they use a smaller learning rate,η= 5×10 −4, and a longer optimization budget.

Trainability and Mode Separation of Mixed IQP-QCBMs The MNIST data-agnostic runs are listed separately because they use a smaller learning rate,η= 5×10 −4, and a longer optimization budget

Reference 61

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Observation fe55c7fe-f745-4b76-8dcb-35834f9226e7 · outbound

This paper cites For the global and data-agnostic initializations, the ancilla branches are sampled uniformly, πℓ = 1 L , ℓ= 0,.

Trainability and Mode Separation of Mixed IQP-QCBMs For the global and data-agnostic initializations, the ancilla branches are sampled uniformly, πℓ = 1 L , ℓ= 0,

Reference 62

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Observation 7bb2a7c4-87e8-42cb-90b8-425315d127e1 · outbound

This paper cites The RBM family also admits quantum extensions with quantified expressivity relations to its classical form [44]; here it serves purely as a classical reference.

Trainability and Mode Separation of Mixed IQP-QCBMs The RBM family also admits quantum extensions with quantified expressivity relations to its classical form [44]; here it serves purely as a classical reference

Reference 63

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:14.732998Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 167f99c4-eec8-489c-9577-3596fc3f8d65 · outbound

This paper cites an unresolved cited work.

Trainability and Mode Separation of Mixed IQP-QCBMs Unresolved cited work

Reference 64

Resolution: malformed identifier; no resolver link, observed 2026-07-31T23:47:14.886781Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a129472-109e-48ae-95f7-8ae28a3625d9 · outbound

This paper cites Each ablated branch is therefore a product distribution.

Trainability and Mode Separation of Mixed IQP-QCBMs Each ablated branch is therefore a product distribution

Reference 65

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:15.035263Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f88d30ae-9315-49a8-8238-af4d76d2035e · outbound

This paper cites 3(e)–(h) by kernel bandwidth at each benchmark’s headline mixture size.

Trainability and Mode Separation of Mixed IQP-QCBMs 3(e)–(h) by kernel bandwidth at each benchmark’s headline mixture size

Reference 66

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:15.141791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Coverage vector

Reference resolution

Outbound references

Pith citing papers