Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables | Paper Citation Record

Observation 26647f02-50f4-4a7b-bffb-af906a5f772c · outbound

This paper cites Quantum dynamics simulation of the advection-diffusion equation.Physical Review Research, 7(4):043318, 2025.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum dynamics simulation of the advection-diffusion equation.Physical Review Research, 7(4):043318, 2025

Reference 1

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Observation e658db4e-56b7-4aa2-a890-3cf7acf88f0b · outbound

This paper cites Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters.Communications in Mathematical Physics, 407(1):19, 2026.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters.Communications in Mathematical Physics, 407(1):19, 2026

Reference 2

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Observation 41cd8807-3d7f-4128-b11e-784926179cd3 · outbound

This paper cites Quantum-accelerated multilevel monte carlo methods for stochastic differential equations in mathematical finance.Quantum, 5:481, 2021.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum-accelerated multilevel monte carlo methods for stochastic differential equations in mathematical finance.Quantum, 5:481, 2021

Reference 3

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Observation b48424dc-2750-4258-a5a6-e961e2713867 · outbound

This paper cites Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost.Physical Review Letters, 131:150603, 2023.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost.Physical Review Letters, 131:150603, 2023

Reference 4

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Observation bfc57d79-58ad-4a75-91e4-e8934a2038ad · outbound

This paper cites Berry, Andrew M.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Berry, Andrew M

Reference 5

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Observation d5643417-796f-490f-9ce2-78a4ec277c5a · outbound

This paper cites Berry, Andrew M.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Berry, Andrew M

Reference 6

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Observation 126e2645-9428-47b4-9d90-192278bcf54b · outbound

This paper cites Bramble, Joseph E.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Bramble, Joseph E

Reference 7

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Observation 32561fcf-0a55-4552-8ab8-f06408e7f001 · outbound

This paper cites Bramble, Alfred H.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Bramble, Alfred H

Reference 8

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Observation 8bc239f2-e7b0-4e2f-ba47-ac595a09d150 · outbound

This paper cites Brenner and L.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Brenner and L

Reference 9

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Observation d0208684-79df-448f-9429-5e89219b47e3 · outbound

This paper cites Quantum algorithm and circuit design solving the poisson equation.New Journal of Physics, 15:013021, 2013.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum algorithm and circuit design solving the poisson equation.New Journal of Physics, 15:013021, 2013

Reference 10

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Observation 253c8cb6-dd89-49ff-8078-b2f8e59356b6 · outbound

This paper cites Childs, Robin Kothari, and Rolando D.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Childs, Robin Kothari, and Rolando D

Reference 11

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Observation 0157c64b-5a27-45b3-8b54-67784efe3478 · outbound

This paper cites Childs, Jin-Peng Liu, and Aaron Ostrander.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Childs, Jin-Peng Liu, and Aaron Ostrander

Reference 12

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Observation 4ff22345-0ac1-4d53-a8b3-ab21c1650d42 · outbound

This paper cites Childs and Nathan Wiebe.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Childs and Nathan Wiebe

Reference 13

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Reference 14

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Observation e53505ce-df7c-40cf-81cc-a469fe702f8e · outbound

This paper cites Quantum algorithms revisited.Proceedings of the Royal Society of London.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum algorithms revisited.Proceedings of the Royal Society of London

Reference 15

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Observation 0395f0d2-af0e-4e22-80d6-80565ffee19f · outbound

This paper cites Optimal scaling quantum linear-systems solver via discrete adiabatic theorem.PRX quantum, 3(4):040303, 2022.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Optimal scaling quantum linear-systems solver via discrete adiabatic theorem.PRX quantum, 3(4):040303, 2022

Reference 16

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Observation c8f8baac-62fb-404f-92f6-4acbd6de2fc6 · outbound

This paper cites Quantum algorithm for simulating the wave equation.Physical Review A, 99(1):012323, 2019.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum algorithm for simulating the wave equation.Physical Review A, 99(1):012323, 2019

Reference 17

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Observation 116aa425-741d-48f6-8094-43762c9d57ce · outbound

This paper cites Quantum realization of the finite element method.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum realization of the finite element method

Reference 18

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Observation 25be8045-22c9-4b73-b856-94d30547e2b6 · outbound

This paper cites American mathematical society, 2022.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables American mathematical society, 2022

Reference 19

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Observation ea20a2ca-e0cb-4dfb-adee-39ca51bdfd1e · outbound

This paper cites Time-marching based quantum solvers for time-dependent linear differential equations.Quantum, 7:955, 2023.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Time-marching based quantum solvers for time-dependent linear differential equations.Quantum, 7:955, 2023

Reference 20

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Observation 5f082e8a-b9bd-485d-8f5e-910547880b8f · outbound

This paper cites Floater, Ewald Quak, and Martin Reimers.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Floater, Ewald Quak, and Martin Reimers

Reference 21

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Observation 416b12ee-bdc5-4d22-8c9f-33dac9e1938f · outbound

This paper cites Gander and Martin Neumüller.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Gander and Martin Neumüller

Reference 22

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Observation dbf3f2b5-a38e-4fe9-af20-058ba57c1e42 · outbound

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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Unresolved cited work

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Observation 997df8af-8239-4f52-b638-1a2f30ea7396 · outbound

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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Unresolved cited work

Reference 24

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Observation b5e50960-8ea5-49f5-be0b-0fa261ba3668 · outbound

This paper cites Improved quantum algorithms for fidelity estimation, 2022.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Improved quantum algorithms for fidelity estimation, 2022

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Observation ac6269a3-5481-4fe3-b606-d3ed3f33269b · outbound

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

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics

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Observation d6f9925b-51fc-485d-873c-326650ea3e3d · outbound

This paper cites Springer, 1985.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Springer, 1985

Reference 27

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Observation 56e911cc-3556-42d4-a7d8-58bfb4d4e2e2 · outbound

This paper cites Harrow, Avinatan Hassidim, and Seth Lloyd.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Harrow, Avinatan Hassidim, and Seth Lloyd

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Observation 6718562e-5327-413f-b663-c6cd43bbe954 · outbound

This paper cites Multilevel monte carlo methods.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Multilevel monte carlo methods

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Observation a9ecdab2-9428-4576-8f17-41669bbd7b2a · outbound

This paper cites A space–time multigrid method for parabolic partial differential equations.SIAM Journal on Scientific Computing, 16(4):848–864, 1995.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables A space–time multigrid method for parabolic partial differential equations.SIAM Journal on Scientific Computing, 16(4):848–864, 1995

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Observation 42336668-7842-4a36-adcc-c867e08d41df · outbound

This paper cites Quantum circuits for partial differential equations via schrödingerisation.Quantum, 8:1563, 2024.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum circuits for partial differential equations via schrödingerisation.Quantum, 8:1563, 2024

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Observation a824ea2a-0737-44c0-8d50-5aabcd68c9c2 · outbound

This paper cites Quantum simulation of partial differential equations via schrödingerisation.Physical Review Letters, 133:230602, 2024.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum simulation of partial differential equations via schrödingerisation.Physical Review Letters, 133:230602, 2024

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Observation a51b645f-2106-4785-804d-e651ca7f508a · outbound

This paper cites Transmutation based quantum simulation for non-unitary dynamics, 2026.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Transmutation based quantum simulation for non-unitary dynamics, 2026

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Observation b89590a6-51ed-4bab-8177-8694166cb464 · outbound

This paper cites Alkadri, Kranthi K.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Alkadri, Kranthi K

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Observation 1beeb9d2-2dc6-4db0-a00d-1edef26dfd49 · outbound

This paper cites Improved quantum algorithms for linear and nonlinear differential equations.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Improved quantum algorithms for linear and nonlinear differential equations

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Observation 8002ac18-83ba-4d0d-9245-ffaaca4eb6b5 · outbound

This paper cites From linear differential equations to unitaries: A moment-matching dilation framework with near-optimal quantum algorithms.PRX Quantum, 7(2):020350, 2026.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables From linear differential equations to unitaries: A moment-matching dilation framework with near-optimal quantum algorithms.PRX Quantum, 7(2):020350, 2026

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Observation edc3a75a-d7f9-491a-8715-99c50a143f24 · outbound

This paper cites Toward efficient end-to-end quantum elliptic pde solvers: A multilevel correction algorithm for direct observable estimations, 2026.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Toward efficient end-to-end quantum elliptic pde solvers: A multilevel correction algorithm for direct observable estimations, 2026

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Observation e188fcb1-e3c2-4847-906d-b1d6cec18084 · outbound

This paper cites Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions

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Observation 75407961-f3bd-4e55-ac42-429672f2d905 · outbound

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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum vs

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Observation 1a022ad1-3fe7-4335-ad83-090cacf9c7e6 · outbound

This paper cites On the numerical inversion of the laplace transform of certain holomorphic mappings.Applied Numerical Mathematics, 51(2–3):289–303, 2004.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables On the numerical inversion of the laplace transform of certain holomorphic mappings.Applied Numerical Mathematics, 51(2–3):289–303, 2004

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Observation c97539cb-13df-431b-a570-2c5befe6b6ab · outbound

This paper cites A spectral order method for inverting sectorial laplace transforms.SIAM Journal on Numerical Analysis, 44(3):1332–1350, 2006.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables A spectral order method for inverting sectorial laplace transforms.SIAM Journal on Numerical Analysis, 44(3):1332–1350, 2006

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Observation 2380cb06-bf4c-4670-9f45-9ae28fbb5b44 · outbound

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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Unresolved cited work

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Observation b0c31a13-5529-4181-b982-5b6257ddfae8 · outbound

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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Unresolved cited work

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Observation 216e971f-f120-4109-a64d-1576e245de96 · outbound

This paper cites Quantum circuits for partial differential equations in fourier space.Physical Review Research, 7:043326, 2025.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum circuits for partial differential equations in fourier space.Physical Review Research, 7:043326, 2025

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Observation a252ae30-c66c-4eea-8bd3-75c54bf9a64d · outbound

This paper cites Iterative methods for shifted positive definite linear systems and time discretization of the heat equation.ANZIAM Journal, 53:134–155, 2011.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Iterative methods for shifted positive definite linear systems and time discretization of the heat equation.ANZIAM Journal, 53:134–155, 2011

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Observation f401edf6-3e3a-4455-9945-c1b3d175ca8b · outbound

This paper cites Quantum algorithms and the finite element method.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum algorithms and the finite element method

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Observation d6e6ca35-76c9-480d-a544-5bb44c40d422 · outbound

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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Unresolved cited work

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Observation d31cde11-43fa-49cb-9c7d-83db69ccd56e · outbound

This paper cites Quantum algorithms for estimating physical quantities using block-encodings.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum algorithms for estimating physical quantities using block-encodings

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Observation d7781fb3-8b56-4095-8ce2-4dd6fe3278fc · outbound

This paper cites A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature.Mathematics of Computation, 69(229):177–195, 2000.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature.Mathematics of Computation, 69(229):177–195, 2000

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Observation a5279584-56a9-4ba5-8a0c-9f784d281be4 · outbound

This paper cites A parallel method for time discretization of parabolic equations based on laplace transformation and quadrature.IMA Journal of Numerical Analysis, 23(2):269–299, 2003.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables A parallel method for time discretization of parabolic equations based on laplace transformation and quadrature.IMA Journal of Numerical Analysis, 23(2):269–299, 2003

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Resolution: unresolved; no resolver link, observed 2026-08-01T16:11:28.603283Z

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Observation 61dd3954-c08b-45ea-a09b-424c55ee5ae5 · outbound

This paper cites Piecewise linear (pre-)wavelets on non-uniform meshes.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Piecewise linear (pre-)wavelets on non-uniform meshes

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Observation 0b634b3c-ed4f-44a2-9f86-e20362bef932 · outbound

This paper cites Quantum algorithms based on the block-encoding framework for matrix functions by contour integrals.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum algorithms based on the block-encoding framework for matrix functions by contour integrals

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Observation 15371267-4a8d-4160-89d1-64b673630c42 · outbound

This paper cites Springer, Berlin, 2 edition, 2006.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Springer, Berlin, 2 edition, 2006

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Observation f7873521-d70f-4fcf-afa2-122fef70a7eb · outbound

This paper cites Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition

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Observation 53661a50-f18e-463d-b62f-c06bc5cfdde6 · outbound

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Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Unresolved cited work

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Observation 5362bd19-9af6-4b81-a1c3-19451c49040d · outbound

This paper cites First, Rory Johnston, Jeremy Tillay, Skylar Chaney, Matthias Rosenkranz, and Michael Lubasch.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables First, Rory Johnston, Jeremy Tillay, Skylar Chaney, Matthias Rosenkranz, and Michael Lubasch

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Observation 42a2850e-6c15-462c-b785-471aab2f9c9a · outbound

This paper cites Iterative methods by space decomposition and subspace correction.SIAM Review, 34(4):581–613, 1992.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Iterative methods by space decomposition and subspace correction.SIAM Review, 34(4):581–613, 1992

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Observation 0f87ab1c-5514-402f-a0c4-4b66881c84c1 · outbound

This paper cites Circuit-efficient randomized quantum simulation of non-unitary dynamics with observable-driven and symmetry-aware designs, 2025.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables Circuit-efficient randomized quantum simulation of non-unitary dynamics with observable-driven and symmetry-aware designs, 2025

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-01T16:11:28.646781Z

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Observation 19cd28a4-8f2e-4be1-bd0c-b5fdbaf8f959 · outbound

This paper cites On the multi-level splitting of finite element spaces.Numerische Mathematik, 49:379–412, 1986.

Exponential Reduction of Mesh Dependence in Quantum Estimation of Parabolic PDE Observables On the multi-level splitting of finite element spaces.Numerische Mathematik, 49:379–412, 1986

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-01T16:11:28.651675Z

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