Paper Citation Record · LEDGER

A Spectral Quantum Algorithm for Numerical Differentiation and Integration

As of 18 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2506.19959.

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

pith.paper-citation-record.v1
2506.19959 v3

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:33:15.629742Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

45 of 45 outbound references displayed

verified exact2
verified fuzzy32
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c1ca6c7b-d9b4-47c6-a532-e737a2cdc55d · outbound

This paper cites Hybrid Quantum/Classical Derivative Theory: Analytical Gradients and Excited-State Dynamics for the Multistate Contracted Variational Quantum Eigensolver,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Hybrid Quantum/Classical Derivative Theory: Analytical Gradients and Excited-State Dynamics for the Multistate Contracted Variational Quantum Eigensolver,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.445789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0f78e19d-d42d-41ac-9c67-ac0c75d94b52 · outbound

This paper cites Calculating energy derivatives for quantum chemistry on a quan- tum computer,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Calculating energy derivatives for quantum chemistry on a quan- tum computer,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.428973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 52554842-7b87-4661-948b-0b4c59705913 · outbound

This paper cites Theory of analytical energy derivatives for the variational quantum eigensolver,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Theory of analytical energy derivatives for the variational quantum eigensolver,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.412356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 51145fe3-0ce2-4430-9c45-21598d85bfd4 · outbound

This paper cites an unresolved cited work.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:33:16.395809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c5519e0c-5ad7-4991-aeb9-b952010efb6b · outbound

This paper cites Pure quantum gradient descent algorithm and full quantum variational eigensolver,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Pure quantum gradient descent algorithm and full quantum variational eigensolver,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.379125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8e4b2370-1eba-484c-897d-eca266afe998 · outbound

This paper cites Quantum algorithmic differentiation,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum algorithmic differentiation,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.362730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c2fad31c-34c2-4194-bb96-666ec822adf0 · outbound

This paper cites Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T18:33:15.444259Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e0bdbe1-631c-47f7-ab84-e66231c3dfba · outbound

This paper cites Quantum supersampling,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum supersampling,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.346428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation db25ee7b-fb91-404b-b6a8-d9424b41bf9c · outbound

This paper cites Quantum Coin Method for Numerical Integration,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum Coin Method for Numerical Integration,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.330179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d5a39e84-cfac-44b8-9fd2-a43931f0d0a2 · outbound

This paper cites Fast Quantum Algorithm for Numerical Gradient Estimation,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Fast Quantum Algorithm for Numerical Gradient Estimation,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.313160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation be5e1b51-2e7c-4660-805c-8d935dfd73f4 · outbound

This paper cites Efficient quantum algorithm for weighted partial sums and numerical integration.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Efficient quantum algorithm for weighted partial sums and numerical integration

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:33:15.831606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation aa22a25c-8d4f-4c00-9e30-14b60ec8e15f · outbound

This paper cites Quantum algorithms and circuits for scientific computing,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum algorithms and circuits for scientific computing,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.297360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 20b4313c-465d-432d-adf5-610920eb013c · outbound

This paper cites Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.281839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7b66565c-41f6-4393-9890-330e6eaf773f · outbound

This paper cites Henrard, Algorithmic Differentiation in Finance Explained.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Henrard, Algorithmic Differentiation in Finance Explained

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.266176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7923d414-e496-4510-a56d-a6a35076d538 · outbound

This paper cites Quantum algorithm and circuit design solving the Poisson equation,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum algorithm and circuit design solving the Poisson equation,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.251367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fc8921e9-5598-4b24-9a71-c151aea00f96 · outbound

This paper cites Quantum Algorithms for Scientific Computing and Approximate Optimization.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum Algorithms for Scientific Computing and Approximate Optimization

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T18:33:15.487165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e3a33f0-1d25-4d80-8a57-2131eb254cc3 · outbound

This paper cites Geometry optimization,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Geometry optimization,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.235085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 38ffe231-9eee-415b-b688-a8a925730d3f · outbound

This paper cites Molecular Vibrations,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Molecular Vibrations,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.218571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ad25b667-92ae-4bb8-b68b-e2dc1e9beb4f · outbound

This paper cites Analytical Derivative Methods in Quantum Chemistry,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Analytical Derivative Methods in Quantum Chemistry,

Reference 19

Resolution: verified exact; doi, observed 2026-08-15T18:33:15.668016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7fc9b812-6eab-4996-bfc3-9b8170d932f9 · outbound

This paper cites an unresolved cited work.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:33:16.202050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2ec88ab2-c415-46bb-9202-1490a6264f42 · outbound

This paper cites The theory of variational hybrid quantum-classical algorithms,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration The theory of variational hybrid quantum-classical algorithms,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.186679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5c3b6b1d-d747-4265-8df9-1a8ce25f6a4c · outbound

This paper cites Progress towards practical quantum variational algorithms,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Progress towards practical quantum variational algorithms,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.169100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a9689ff5-15cb-4733-bb8f-4bc3f40e2071 · outbound

This paper cites Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.154335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a2f7a07c-daf2-41ed-b7bd-b4cde2f471fa · outbound

This paper cites Numerical Approximation of Predictive Distribution,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Numerical Approximation of Predictive Distribution,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.138892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4b9fa757-6428-471f-af80-6762df3a967f · outbound

This paper cites Fast quantum algorithms for numerical integrals and stochastic processes,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Fast quantum algorithms for numerical integrals and stochastic processes,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.123119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 870bcb04-99fe-4948-ab5b-1bb1e017336c · outbound

This paper cites Review of quantum Monte Carlo methods and their applications,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Review of quantum Monte Carlo methods and their applications,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.107140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9b96bc1c-0062-4130-9022-36f73209b809 · outbound

This paper cites Quantum integration in Sobolev classes,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum integration in Sobolev classes,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.090607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 90a78028-dc1c-495b-b15d-d969cfd8a0f2 · outbound

This paper cites A general quantum algorithm for numerical integration,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration A general quantum algorithm for numerical integration,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.074406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 63bacc10-5c8c-4733-b01a-34024d1b2fef · outbound

This paper cites Quantum search algorithm on weighted databases,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum search algorithm on weighted databases,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.059093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f399b150-410e-4cd6-9c0c-5d6e420d8ae8 · outbound

This paper cites Path integration in non-relativistic quan- tum mechanics,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Path integration in non-relativistic quan- tum mechanics,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.043882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d09f9a99-e3e3-4671-b19c-da3ad5897f88 · outbound

This paper cites Notes on FFT-based differentiation,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Notes on FFT-based differentiation,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.028404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b49c5eb6-15ed-46d5-97ca-73bea2d5458c · outbound

This paper cites Calculating numerical derivatives using Fourier transform: some pitfalls and how to avoid them,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Calculating numerical derivatives using Fourier transform: some pitfalls and how to avoid them,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:16.011615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 09d92945-2f1e-4a4f-abfb-dcbeceeea6f3 · outbound

This paper cites Kreyszig, H.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Kreyszig, H

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:15.995062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c5a9a236-02bb-4610-a0d9-0385af4f5a57 · outbound

This paper cites an unresolved cited work.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:33:15.979663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0c7b6855-8b51-4fe7-aeee-047e637930b7 · outbound

This paper cites Block encoding of matrix product operators,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Block encoding of matrix product operators,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:15.964084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c18ff6c5-cf4e-4227-9454-d6109318d497 · outbound

This paper cites Quantum circuits for isometries,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum circuits for isometries,

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:15.948401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3bcb714d-75ca-4a85-a175-0968b1e949c4 · outbound

This paper cites Explicit Quantum Circuits for Block Encod- ings of Certain Sparse Matrices,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Explicit Quantum Circuits for Block Encod- ings of Certain Sparse Matrices,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:15.932170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5aebd088-a975-4426-8c42-c0a240f75eab · outbound

This paper cites Simulating Sparse Hamiltonians with Star Decompositions,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Simulating Sparse Hamiltonians with Star Decompositions,

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:15.915033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 029ae612-1ad3-4213-9dfd-1dfd7107436c · outbound

This paper cites Hamiltonian Simulation by Qubitization.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Hamiltonian Simulation by Qubitization

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T18:33:15.597570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b230d67-4d84-4386-860f-3cd83eea7f58 · outbound

This paper cites On Encoding Matrices using Quantum Circuits,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration On Encoding Matrices using Quantum Circuits,

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T18:33:15.603445Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02af975c-a991-4b3f-9530-b0521158689f · outbound

This paper cites Multidimensional Quantum Fourier Transformation.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Multidimensional Quantum Fourier Transformation

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T18:33:15.608930Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 628613b8-0ca5-47f2-8b3a-0071b79d0c41 · outbound

This paper cites Quantum computing with Qiskit.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Quantum computing with Qiskit

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T18:33:15.614617Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c9b1936-20ea-4b88-9643-22494227b281 · outbound

This paper cites an unresolved cited work.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:33:15.898448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4453f3fe-675c-4929-9adf-31e1cdd776e6 · outbound

This paper cites 3.6 Numerical Integration - Calculus Volume 2|OpenStax,.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration 3.6 Numerical Integration - Calculus Volume 2|OpenStax,

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:33:15.881820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 90ea48ce-8a1c-4119-a5ea-2729b857326a · outbound

This paper cites an unresolved cited work.

A Spectral Quantum Algorithm for Numerical Differentiation and Integration Unresolved cited work

Reference 2016

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:33:15.866016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.