Paper Citation Record · LEDGER

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

As of 10 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 7 inbound Pith citation observations for arXiv:2509.02429.

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

pith.paper-citation-record.v1
2509.02429 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:51:15.959187Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

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

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T04:31:22.336028Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T23:26:22.696151Z

Reference resolution

25 of 25 outbound references displayed

verified exact1
verified fuzzy21
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ecbd8bc7-daef-458d-8125-be757f10d211 · outbound

This paper cites Partial differential equations.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Partial differential equations

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.564953Z

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 a0b1a4d9-1a11-4e8e-b10c-3bbb3395fcf8 · outbound

This paper cites Numerical solution of partial differential equations: Finite difference methods.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Numerical solution of partial differential equations: Finite difference methods

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.551545Z

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 c8d59a2a-4112-45a1-b390-999ec32d3a76 · outbound

This paper cites Numerical partial differential equations: Finite difference methods.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Numerical partial differential equations: Finite difference methods

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.538423Z

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

Observation 796e92ec-ba44-43f2-9cd9-a6db5b511b32 · outbound

This paper cites Solving ordinary differential equations II.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Solving ordinary differential equations II

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.525175Z

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 bf27ab80-bb72-421f-9cc7-a440fa4fce33 · outbound

This paper cites Krylov subspace methods for linear systems.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Krylov subspace methods for linear systems

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.512045Z

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 391a8541-09f4-43a8-9d69-cc18241c135b · outbound

This paper cites Hamiltonian simulation by qubitization.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Hamiltonian simulation by qubitization

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.498594Z

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 7fbfc813-1225-42ca-b158-35ee104ad40e · outbound

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

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.485540Z

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 ae663bcb-007a-4c82-b115-e624056ad437 · outbound

This paper cites Efficient quantum algorithms for simulating sparse Hamiltonians.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Efficient quantum algorithms for simulating sparse Hamiltonians

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.472510Z

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 5296c81b-50da-4d57-895a-f02e06bbddbe · outbound

This paper cites Hamiltonian simulation with nearly opti- mal dependence on all parameters.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Hamiltonian simulation with nearly opti- mal dependence on all parameters

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.459233Z

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 8132eaf5-6a0f-4320-bbf8-2e2d6e866a35 · outbound

This paper cites Quantum algorithm for systems of linear equations with exponentially improved dependence on precision.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Quantum algorithm for systems of linear equations with exponentially improved dependence on precision

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.446233Z

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 f8c6303c-bb60-4851-b5bd-7c8cd16cc964 · outbound

This paper cites Explicit quantum circuits for block encodings of certain sparse matrices.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Explicit quantum circuits for block encodings of certain sparse matrices

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.433019Z

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 e444625f-fe40-410d-9798-62e588f625d1 · outbound

This paper cites Ex- plicit block encodings of boundary value problems for many-body elliptic operators.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Ex- plicit block encodings of boundary value problems for many-body elliptic operators

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.419171Z

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 4912fb83-18c0-441b-baca-7bce945db71b · outbound

This paper cites Optimal Hamiltonian simulation by quantum signal processing.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Optimal Hamiltonian simulation by quantum signal processing

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.405699Z

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 82177962-8613-4905-964f-cc0ea4820425 · outbound

This paper cites Grand unification of quantum algorithms.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Grand unification of quantum algorithms

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.391839Z

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 ec8d2d9a-acd5-48c7-a18a-154a8c01fa55 · outbound

This paper cites Quantum computation and quantum information.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Quantum computation and quantum information

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.378469Z

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 3f97e632-8f22-4575-b2a7-0e23840d9bef · outbound

This paper cites Quantum computing: A gentle introduction.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Quantum computing: A gentle introduction

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.364410Z

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

Observation fe17a104-96cd-489d-bfe5-9ad2a568f54f · outbound

This paper cites Lecture notes on quantum algorithms for scientific computation.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Lecture notes on quantum algorithms for scientific computation

Reference 17

Resolution: verified exact; raw_fallback, observed 2026-08-05T11:51:16.445601Z

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 192d1439-3b51-4ac1-9300-ddf21c80410f · outbound

This paper cites Quantum error correction for quantum memories.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Quantum error correction for quantum memories

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.349677Z

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 5fc51ae4-cac3-4b26-9891-a016e65d60cc · outbound

This paper cites Expressing and Analyzing Quantum Algorithms with Qualtran.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Expressing and Analyzing Quantum Algorithms with Qualtran

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-05T11:51:15.418367Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e883e7a-0c21-457e-a66d-4fdb222032f9 · outbound

This paper cites A logarithmic- depth quantum carry-lookahead adder.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian A logarithmic- depth quantum carry-lookahead adder

Reference 20

Resolution: metadata mismatch; raw_fallback, observed 2026-08-05T11:51:16.269012Z

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 0a4b08d4-1788-4c28-9521-3a45cfa812f1 · outbound

This paper cites Improved quantum circuits for elliptic curve discrete logarithms.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Improved quantum circuits for elliptic curve discrete logarithms

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.205151Z

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 1c4b52a1-156e-447e-8540-8222eacefc91 · outbound

This paper cites Block-encoding structured matrices for data input in quantum computing.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Block-encoding structured matrices for data input in quantum computing

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:17.008373Z

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 8d3e6cf7-a0bc-40e3-bbe7-ba39f359c4eb · outbound

This paper cites FABLE: Fast approximate quantum circuits for block-encodings.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian FABLE: Fast approximate quantum circuits for block-encodings

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:16.825982Z

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 c3ada77f-1fbe-4944-a008-16671f993988 · outbound

This paper cites Realization of quantum signal processing on a noisy quantum computer.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Realization of quantum signal processing on a noisy quantum computer

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:51:16.605189Z

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

Observation fc35a1ad-abaa-4857-abd1-eaf0e1459451 · outbound

This paper cites Resource-efficient variational block-encoding.

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian Resource-efficient variational block-encoding

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-05T11:51:15.959187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 1d651e96-33f3-4d1b-9b05-dde172f6596d · inbound

TARE: Block Encoding Linear Combinations of Pauli Strings Without Ancilla State Preparation cites this paper.

TARE: Block Encoding Linear Combinations of Pauli Strings Without Ancilla State Preparation Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-16T16:28:05.621597Z

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

Observation 11036938-e981-4185-96d7-d78d9986dea7 · inbound

Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions cites this paper.

Explicit Block Encodings of Discrete Laplacians with Mixed Boundary Conditions Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-15T11:40:31.908786Z

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 820ce7a0-462a-4d01-8739-7f61098858e8 · inbound

Explicit Block Encoding of Difference-of-Gaussian Operators on a Periodic Grid cites this paper.

Explicit Block Encoding of Difference-of-Gaussian Operators on a Periodic Grid Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-11T08:20:57.780546Z

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 568edf48-0671-4ab8-b817-913d063cbc8e · inbound

Block-encodings as programming abstractions: The Eclipse Qrisp BlockEncoding Interface cites this paper.

Block-encodings as programming abstractions: The Eclipse Qrisp BlockEncoding Interface Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

Reference 68

Resolution: verified exact; arxiv_id, observed 2026-05-10T12:05:23.573541Z

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 2905868b-c177-4454-9a81-f83aecb2b5c1 · inbound

Unitaria: Quantum Linear Algebra via Block Encodings cites this paper.

Unitaria: Quantum Linear Algebra via Block Encodings Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-12T05:56:33.148381Z

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 5d5e2aae-20b5-4aba-ad90-55bfec2374bd · inbound

Pauli-structured preconditioning for quantum linear system solvers cites this paper.

Pauli-structured preconditioning for quantum linear system solvers Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-07-01T23:26:22.697667Z

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 d33764c9-f9e1-4279-9623-5e0efcb42d84 · inbound

Moment-Structured Block Encodings of Periodic Finite-Difference Operators cites this paper.

Moment-Structured Block Encodings of Periodic Finite-Difference Operators Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T04:31:22.336028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.