Paper Citation Record · LEDGER

Linearization Scheme of Shallow Water Equations for Quantum Algorithms

As of 23 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 0 inbound Pith citation observations for arXiv:2506.22345.

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

pith.paper-citation-record.v1
2506.22345 v1

Coverage vector

measured 52 of 52 reference resolution

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Outbound references

Observation db2a585e-c331-496d-9b37-6b0f8a9d3708 · outbound

This paper cites an unresolved cited work.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 1

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Observation c4440b58-6820-4875-a3ab-d826828fd605 · outbound

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 2

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Observation a9d7fc3e-b1ab-4b7a-8d86-83362890c692 · outbound

This paper cites (14): F (1)f + F (2)f [2] + F (3)f [3] +.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms (14): F (1)f + F (2)f [2] + F (3)f [3] +

Reference 3

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Observation 3e4c7ea7-2b85-403c-9a94-6a269a976af8 · outbound

This paper cites (3), the streaming matrix is built by first defining a matrix S such that: Sf = −c · ∇f (20) With x as the partial coordinate, in 1D this is equivalent to Sf =  .

Linearization Scheme of Shallow Water Equations for Quantum Algorithms (3), the streaming matrix is built by first defining a matrix S such that: Sf = −c · ∇f (20) With x as the partial coordinate, in 1D this is equivalent to Sf =  

Reference 4

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 5

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 6

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Observation 176910ef-24d0-42ec-8db2-642b7b832101 · outbound

This paper cites First, the initial quantum state |b⟩ must be prepared efficiently.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms First, the initial quantum state |b⟩ must be prepared efficiently

Reference 7

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Observation 241b85ac-8fa9-4144-bfa3-e4d74f9cad7d · outbound

This paper cites (A2) Then for the degree ( j), we define a vector for all grid points: F (j)(x) = F (j)(x1), ...,F (j)(xN ) T (A3) We further define a replacement transfer matrix for Eq.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms (A2) Then for the degree ( j), we define a vector for all grid points: F (j)(x) = F (j)(x1), ...,F (j)(xN ) T (A3) We further define a replacement transfer matrix for Eq

Reference 8

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 9

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 10

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 11

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 12

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 13

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 14

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Observation dc405b18-b0f7-44e5-9e01-5a7e5d4f0aea · outbound

This paper cites Succi, W.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Succi, W

Reference 15

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Observation 154dde51-fd13-41d1-b5ed-3f36ae3b219e · outbound

This paper cites Aaronson, Read the fine print, Nature Physics 11, 291 (2015).

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Aaronson, Read the fine print, Nature Physics 11, 291 (2015)

Reference 16

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Observation c6f4f19d-63ef-408f-9eb6-835f0535aaeb · outbound

This paper cites Simulating fluid flows with quantum computing.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Simulating fluid flows with quantum computing

Reference 17

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Observation 78220e25-2be5-4cb9-af81-8edca8de2b1c · outbound

This paper cites Yepez, Quantum computation of fluid dynamics, in NASA International Conference on Quantum Computing and Quantum Communications(Springer, 1998) pp.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Yepez, Quantum computation of fluid dynamics, in NASA International Conference on Quantum Computing and Quantum Communications(Springer, 1998) pp

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:12:33.599089Z

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Observation 293f73ab-5721-4d52-bde6-99ece4a08aa7 · outbound

This paper cites Gaitan, Finding flows of a navier–stokes fluid through quantum computing, npj Quantum Information 6, 61 (2020).

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Gaitan, Finding flows of a navier–stokes fluid through quantum computing, npj Quantum Information 6, 61 (2020)

Reference 19

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Observation c1162dbd-929a-48b9-adda-21cca74d7745 · outbound

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 20

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Observation 6ff09313-1a25-4c43-89de-1f311b6098ea · outbound

This paper cites Meng and Y.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Meng and Y

Reference 21

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Observation b9872803-0a64-4a83-9b57-ba9cf0b8d3a4 · outbound

This paper cites Vadasz, Rendering the navier–stokes equations for a compressible fluid into the schr¨ odinger equation for quan- tum mechanics, Fluids 1 (2016).

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Vadasz, Rendering the navier–stokes equations for a compressible fluid into the schr¨ odinger equation for quan- tum mechanics, Fluids 1 (2016)

Reference 22

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Observation b0688284-f2e6-4775-9604-a654da4c498f · outbound

This paper cites Syamlal, C.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Syamlal, C

Reference 23

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 24

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Observation 0c474b57-b568-47d1-93d0-f8e67096c637 · outbound

This paper cites Sanavio and S.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Sanavio and S

Reference 25

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Observation 5722ff26-e84b-4682-a391-638ba27e21de · outbound

This paper cites Quantum Carleman Lattice Boltzmann Simulation of Fluids.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Quantum Carleman Lattice Boltzmann Simulation of Fluids

Reference 26

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Observation 2f3eb572-a4fb-44f0-a734-6845469d7a03 · outbound

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Itani and S

Reference 27

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Observation ad3d7254-5357-4fdb-9a51-1b2cf24c63bb · outbound

This paper cites Quantum Carleman Linearization of the Lattice Boltzmann Equation with Boundary Conditions.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Quantum Carleman Linearization of the Lattice Boltzmann Equation with Boundary Conditions

Reference 28

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 29

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Observation 63fb9585-a44e-47cc-857f-9dc5db40e354 · outbound

This paper cites Kinnmark, The Shallow Water Wave Equations: For- mulation, Analysis and Application(Springer, 1986).

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Kinnmark, The Shallow Water Wave Equations: For- mulation, Analysis and Application(Springer, 1986)

Reference 30

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Observation b6cd3635-7120-44fc-90d3-d0237c8200dc · outbound

This paper cites Salmon, The lattice boltzmann method as a basis for ocean circulation modeling, Journal of Marine Research 57, 503 (1999).

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Salmon, The lattice boltzmann method as a basis for ocean circulation modeling, Journal of Marine Research 57, 503 (1999)

Reference 31

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 32

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Observation 0a812d41-f623-4100-91fe-bc00b344dfba · outbound

This paper cites Zhou, A lattice boltzmann model for the shallow water equations, Computer methods in applied mechanics and engineering 191, 3527 (2002).

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Zhou, A lattice boltzmann model for the shallow water equations, Computer methods in applied mechanics and engineering 191, 3527 (2002)

Reference 33

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Observation a7a6f59e-56a9-4722-ae6c-546351afe857 · outbound

This paper cites van Thang, B.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms van Thang, B

Reference 34

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

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This paper cites Lamb, Horace, Hydrodynamics (Cambridge [Eng.], University Press, 1895) p.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Lamb, Horace, Hydrodynamics (Cambridge [Eng.], University Press, 1895) p

Reference 36

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 37

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Observation 7b07bf6b-8d39-4689-90da-400064ad8b94 · outbound

This paper cites Lecture Notes on Quantum Algorithms for Scientific Computation.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Lecture Notes on Quantum Algorithms for Scientific Computation

Reference 38

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 39

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Observation a0a39327-1118-42af-8d70-18461aaacf42 · outbound

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Gily´ en, Y

Reference 40

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 41

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Observation f259f1a7-dd2a-4e9e-9ef3-e82484123412 · outbound

This paper cites A shortcut to an optimal quantum linear system solver.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms A shortcut to an optimal quantum linear system solver

Reference 42

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Observation 34a39171-8838-43b2-9deb-33833c361d15 · outbound

This paper cites Quantum Linear System Solvers: A Survey of Algorithms and Applications.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Quantum Linear System Solvers: A Survey of Algorithms and Applications

Reference 43

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Quantum algorithms: A survey of applications and end-to-end complexities

Reference 44

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 45

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Observation 8969f316-6d51-46fc-9aa9-d8d774e756bc · outbound

This paper cites Zhang, T.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Zhang, T

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:12:30.229160Z

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Observation 6d8603dc-199c-48d3-a7cd-0766a5854742 · outbound

This paper cites Creating superpositions that correspond to efficiently integrable probability distributions.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Creating superpositions that correspond to efficiently integrable probability distributions

Reference 47

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Observation e30c603e-b0f4-42fb-a33a-7e8a3ab84495 · outbound

This paper cites Wavefunction preparation and resampling using a quantum computer.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Wavefunction preparation and resampling using a quantum computer

Reference 48

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Linearization Scheme of Shallow Water Equations for Quantum Algorithms Unresolved cited work

Reference 49

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Observation 691304d2-fc09-4a5d-bfd0-8dedd26cb1ab · outbound

This paper cites Gonzalez-Conde, T.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Gonzalez-Conde, T

Reference 50

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Observation df0a4d66-dd9d-4d43-bbed-af33fe73fa60 · outbound

This paper cites Iaconis, S.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Iaconis, S

Reference 51

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This paper cites Jaques and A.

Linearization Scheme of Shallow Water Equations for Quantum Algorithms Jaques and A

Reference 52

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