Paper Citation Record · LEDGER

Quantum Natural Gradient

As of 15 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 7 inbound Pith citation observations for arXiv:1909.02108.

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

pith.paper-citation-record.v1
1909.02108 v3

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T05:09:38.567787Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-12T10:07:59.312011Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T13:15:45.240245Z

Reference resolution

36 of 36 outbound references displayed

verified exact6
verified fuzzy3
unresolved26
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9d05be3f-f1cd-4dc8-aa44-4be4f214f081 · outbound

This paper cites Natural gradient works eﬃciently in learning.

Quantum Natural Gradient Natural gradient works eﬃciently in learning

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.431425Z

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Observation f99d630d-574f-4b6f-8872-f436912c0e19 · outbound

This paper cites PennyLane: Automatic differentiation of hybrid quantum-classical computations.

Quantum Natural Gradient PennyLane: Automatic differentiation of hybrid quantum-classical computations

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.436637Z

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Observation 23aa7502-2f03-438b-a5fe-b6079a6bb3c9 · outbound

This paper cites Geometric speed limit of accessible many-body state preparation.

Quantum Natural Gradient Geometric speed limit of accessible many-body state preparation

Reference 3

Resolution: verified exact; doi, observed 2026-08-14T05:09:38.739862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 78d47f9d-bbba-4e9c-8376-e11814814355 · outbound

This paper cites Localization and glassy dynamicsofmany-bodyquantumsystems.

Quantum Natural Gradient Localization and glassy dynamicsofmany-bodyquantumsystems

Reference 4

Resolution: verified exact; doi, observed 2026-08-14T05:09:38.729170Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 70e4eaba-099d-4fe2-8405-6b2db32cba92 · outbound

This paper cites Light-cone eﬀect and supersonic correlations in one-and two-dimensional bosonic superﬂuids.

Quantum Natural Gradient Light-cone eﬀect and supersonic correlations in one-and two-dimensional bosonic superﬂuids

Reference 5

Resolution: verified exact; doi, observed 2026-08-14T05:09:38.717426Z

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Observation d29c651d-076e-4643-93d3-843922ea7885 · outbound

This paper cites Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor.

Quantum Natural Gradient Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:09:38.871714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9a5e63dd-464d-442e-8170-8dc57dbc8eb4 · outbound

This paper cites Efficient quantum measurement of Pauli operators in the presence of finite sampling error.

Quantum Natural Gradient Efficient quantum measurement of Pauli operators in the presence of finite sampling error

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.456809Z

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Observation 252f4d6a-1513-4168-8fa7-a40253ba250d · outbound

This paper cites The Expressive Power of Parameterized Quantum Circuits.

Quantum Natural Gradient The Expressive Power of Parameterized Quantum Circuits

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.460404Z

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Observation 457b5001-70d2-4754-b263-04f92116ab05 · outbound

This paper cites Classification with Quantum Neural Networks on Near Term Processors.

Quantum Natural Gradient Classification with Quantum Neural Networks on Near Term Processors

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.464411Z

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Observation e75382e1-6dee-4956-b64d-a2da4d151256 · outbound

This paper cites A Quantum Approximate Optimization Algorithm.

Quantum Natural Gradient A Quantum Approximate Optimization Algorithm

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.468746Z

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Observation 08f1285c-96c5-4c16-9d3a-21cf9fe8f6ff · outbound

This paper cites Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families.

Quantum Natural Gradient Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.472556Z

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Observation c191abf7-8f5a-4aa9-a46e-d1c352e09108 · outbound

This paper cites Practical optimization for hybrid quantum-classical algorithms.

Quantum Natural Gradient Practical optimization for hybrid quantum-classical algorithms

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.476528Z

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Unavailable: canonical work link unavailable.

Observation 274fb39a-3609-4694-8be6-0e792dd32fff · outbound

This paper cites Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms.

Quantum Natural Gradient Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.481184Z

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Observation 5f9bc4e0-80a1-4cee-9f17-1a4c01cb5ecf · outbound

This paper cites Towards quantum machine learning with tensor networks.Quantum Science and Technology, 4:024001, 2018.

Quantum Natural Gradient Towards quantum machine learning with tensor networks.Quantum Science and Technology, 4:024001, 2018

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.485766Z

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Observation c337c917-3b50-45fa-ada0-1014f1ea8d40 · outbound

This paper cites Three Factors Influencing Minima in SGD.

Quantum Natural Gradient Three Factors Influencing Minima in SGD

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.489996Z

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Observation c5f578fc-dc6c-4ecf-a2e0-6cb510d86b97 · outbound

This paper cites Robust quantum compilation and circuit optimisation via energy minimisation.

Quantum Natural Gradient Robust quantum compilation and circuit optimisation via energy minimisation

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.494504Z

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Observation 96ecb239-8867-4e61-8ee4-f1f513ebd631 · outbound

This paper cites Variational quantum algorithms for discovering hamiltonian spectra.Physical Review A, 99(6):062304, 2019.

Quantum Natural Gradient Variational quantum algorithms for discovering hamiltonian spectra.Physical Review A, 99(6):062304, 2019

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.498382Z

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Observation 7004fd3b-478a-4f60-87db-b4ccdad0752f · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Quantum Natural Gradient Adam: A Method for Stochastic Optimization

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.501939Z

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Observation 4f21bc30-5164-4960-a993-9b523b505559 · outbound

This paper cites Geometry and non- adiabatic response in quantum and classical systems.

Quantum Natural Gradient Geometry and non- adiabatic response in quantum and classical systems

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.505432Z

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Observation a0569a92-cee9-4fa5-9b09-a6f92555a014 · outbound

This paper cites Springer, 1981.

Quantum Natural Gradient Springer, 1981

Reference 20

Resolution: verified exact; doi, observed 2026-08-14T05:09:38.684779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 11a09ce2-5628-41d8-8df8-fe023cb37b8d · outbound

This paper cites Eﬃcient variational quantum simulator incorporating active error minimization.

Quantum Natural Gradient Eﬃcient variational quantum simulator incorporating active error minimization

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.512176Z

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Observation b3ccd8d3-b6bc-4b6b-9d87-3e4faa41957c · outbound

This paper cites Fisher-rao metric, ge- ometry, and complexity of neural networks.

Quantum Natural Gradient Fisher-rao metric, ge- ometry, and complexity of neural networks

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:09:38.918020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 211e172d-33bc-4a59-8a26-9fa03c7ffca3 · outbound

This paper cites Varia- tional ansatz-based quantum simulation of imaginary time evolution.npj Quantum Information, 5(1):1–6, 2019.

Quantum Natural Gradient Varia- tional ansatz-based quantum simulation of imaginary time evolution.npj Quantum Information, 5(1):1–6, 2019

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.519559Z

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Observation 155f24ae-109f-4f34-a5f4-c1f2805d2d61 · outbound

This paper cites Barren plateaus in quantum neural network training landscapes.Nature communications, 9(1): 4812, 2018.

Quantum Natural Gradient Barren plateaus in quantum neural network training landscapes.Nature communications, 9(1): 4812, 2018

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.523316Z

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Observation b9a13dba-0ce5-4f79-a321-faff3ed39658 · outbound

This paper cites Quantumcircuitlearning.

Quantum Natural Gradient Quantumcircuitlearning

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.527428Z

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Observation 27282a39-c085-48de-be52-589f15d10d5f · outbound

This paper cites Path-SGD: Path-normalized optimization in deep neural networks.

Quantum Natural Gradient Path-SGD: Path-normalized optimization in deep neural networks

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:09:38.906353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8334506b-478b-4af0-8748-66d28fc4ddb7 · outbound

This paper cites A variational eigenvalue solver on a photonic quantum processor.

Quantum Natural Gradient A variational eigenvalue solver on a photonic quantum processor

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.534314Z

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Observation 10a3015f-e84e-43d6-826c-726382627d03 · outbound

This paper cites Information-geometry of quantum states.

Quantum Natural Gradient Information-geometry of quantum states

Reference 28

Resolution: verified exact; doi, observed 2026-08-14T05:09:38.641703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f317ec49-76f4-48e2-ae44-d41e306d6e2f · outbound

This paper cites Quantum computing in the NISQ era and beyond.Quantum, 2:79, 2018.

Quantum Natural Gradient Quantum computing in the NISQ era and beyond.Quantum, 2:79, 2018

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.541677Z

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Observation a69ea921-07db-4445-af76-5171c96a9e3b · outbound

This paper cites Circuit-centric quantum classifiers.

Quantum Natural Gradient Circuit-centric quantum classifiers

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.546044Z

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Observation b99c231e-c58e-460c-a9e1-1d44dd4b92c3 · outbound

This paper cites Evaluat- ing analytic gradients on quantum hardware.

Quantum Natural Gradient Evaluat- ing analytic gradients on quantum hardware

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.549998Z

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Observation 13f9a0dd-03bd-4574-858d-8279dc3e4253 · outbound

This paper cites Weak binding between two aromatic rings: Feeling the van der waals attraction by quantum monte carlo methods.The Journal of Chemical Physics, 127(1):014105, 2007.

Quantum Natural Gradient Weak binding between two aromatic rings: Feeling the van der waals attraction by quantum monte carlo methods.The Journal of Chemical Physics, 127(1):014105, 2007

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.553535Z

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Observation 92e5b680-c9f5-4b89-bd32-fc4682ad220b · outbound

This paper cites Multivariate stochastic approximation using a simultaneous perturbation gradient approximation.

Quantum Natural Gradient Multivariate stochastic approximation using a simultaneous perturbation gradient approximation

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.557342Z

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Observation 928e527c-c5e1-4ff4-adb9-2df64ca9e79b · outbound

This paper cites Geometric phases in physics.Geometric Phases In Physics.

Quantum Natural Gradient Geometric phases in physics.Geometric Phases In Physics

Reference 34

Resolution: malformed identifier; no resolver link, observed 2026-08-14T05:09:38.561005Z

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Observation a3edfaf9-dd9a-4018-812b-0db834ed74b6 · outbound

This paper cites PennyLane source code.

Quantum Natural Gradient PennyLane source code

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:09:38.894761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8d5bfe95-831a-4440-812e-82e54813be3c · outbound

This paper cites Theory of variational quantum simulation.Quantum, 3:191, 2019.

Quantum Natural Gradient Theory of variational quantum simulation.Quantum, 3:191, 2019

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-14T05:09:38.567787Z

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Pith citing papers

Observation 6ca69204-8774-411b-addf-3b848837cd6d · inbound

PennyLane: Automatic differentiation of hybrid quantum-classical computations cites this paper.

PennyLane: Automatic differentiation of hybrid quantum-classical computations Quantum Natural Gradient

Reference 62

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T15:14:44.149227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d3e5fc10-b562-4b01-9c55-3938957e67de · inbound

Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States cites this paper.

Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States Quantum Natural Gradient

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-05-18T04:05:50.928542Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 14d21351-1ea9-4fc0-a675-1a0286484ae7 · inbound

Loss-aware state space geometry for quantum variational algorithms cites this paper.

Loss-aware state space geometry for quantum variational algorithms Quantum Natural Gradient

Reference 58

Resolution: verified exact; arxiv_id, observed 2026-05-10T22:35:49.685200Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 647b7e26-be04-486f-bcd3-2783b1fa18a4 · inbound

Evaluating quantum circuits in the reservoir computing paradigm cites this paper.

Evaluating quantum circuits in the reservoir computing paradigm Quantum Natural Gradient

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T16:41:26.355922Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e01355bc-4714-422c-bab1-7f41bb30e4fa · inbound

Evaluating quantum circuits in the reservoir computing paradigm cites this paper.

Evaluating quantum circuits in the reservoir computing paradigm Quantum Natural Gradient

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T13:15:45.241678Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3e7ea8d5-82ef-413e-a07f-cae1c44e932c · inbound

Quantum encodings that preserve persistent homology cites this paper.

Quantum encodings that preserve persistent homology Quantum Natural Gradient

Reference 191

Resolution: verified exact; arxiv_id, observed 2026-06-29T11:53:24.310196Z

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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f59bb16b-ecc1-4143-9cd7-b59259e3e8ad · inbound

Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning cites this paper.

Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning Quantum Natural Gradient

Reference 97

Resolution: malformed identifier; no resolver link, observed 2026-07-12T10:07:59.312011Z

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