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Nana Liu

affiliation not provided to SSRN

SCHOLARLY PAPERS

8

DOWNLOADS

493

TOTAL CITATIONS

4

Scholarly Papers (8)

1.

Quantum Algorithms for Nonlinear Partial Differential Equations

Number of pages: 59 Posted: 10 Feb 2023
Shi Jin and Nana Liu
affiliation not provided to SSRN and affiliation not provided to SSRN
Downloads 217 (371,583)

Abstract:

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nonlinear partial differential equations, Quantum Algorithm, Hamilton-Jacobi equations, Level set methods

2.

Time Complexity Analysis of Quantum Difference Methods for Linear High Dimensional and Multiscale Partial Differential Equations

Number of pages: 40 Posted: 22 Mar 2022
Shi Jin, Nana Liu and Yue Yu
affiliation not provided to SSRN, affiliation not provided to SSRN and Xiangtan University
Downloads 55 (1,010,164)

Abstract:

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Quantum difference methods, Quantum linear algorithms, HHL algorithm, Time complexity, Asymptotic-Preserving schemes

3.

Quantum Circuits for the Heat Equation with Physical Boundary Conditions Via Schrödingerisation

Number of pages: 45 Posted: 02 Aug 2024
Shi Jin, Nana Liu and Yue Yu
affiliation not provided to SSRN, affiliation not provided to SSRN and Xiangtan University
Downloads 50 (1,074,648)

Abstract:

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Schödingerisation, Quantum circuits, Physical boundary conditions, Linear combination of unitaries, Autonomous system, Shift operators

4.

Quantum Preconditioning Method for Linear System Problems Via Schr\"Odingerization

Number of pages: 29 Posted: 17 Jul 2025
Shi Jin, Nana Liu, Chuwen Ma and Yue Yu
affiliation not provided to SSRN, affiliation not provided to SSRN, affiliation not provided to SSRN and Xiangtan University
Downloads 48 (1,097,529)
Citation 2

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Linear algebra problems, Schr\"odingerization, BPX preconditioner, Quantum algorithms

5.

Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions

Number of pages: 25 Posted: 29 May 2023
Shi Jin, Xiantao Li, Nana Liu and Yue Yu
affiliation not provided to SSRN, Pennsylvania State University, affiliation not provided to SSRN and Xiangtan University
Downloads 44 (1,133,231)
Citation 2

Abstract:

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Schrödingerisation, Quantum simulation, Physical boundary conditions, Interface problems, Geometric optics problems

6.

Time Complexity Analysis of Quantum Algorithms Via Linear Representations For  Nonlinear Ordinary and Partial Differential Equations

Number of pages: 60 Posted: 03 Oct 2022
Shi Jin, Nana Liu and Yue Yu
affiliation not provided to SSRN, affiliation not provided to SSRN and Xiangtan University
Downloads 43 (1,145,425)

Abstract:

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Linear representation methods, Liouville representation, Koopman-von Neumann representation, Semiclassical Schrodinger equation, Quantum linear systems algorithms, Quantum simulation

7.

Schro¨dingerization based quantum algorithms for the time-fractional heat equation

Number of pages: 31 Posted: 24 Sep 2025
Shi Jin, Nana Liu and Yue Yu
affiliation not provided to SSRN, affiliation not provided to SSRN and Xiangtan University
Downloads 31 (1,332,057)

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fractional heat equation, gradient flow, quantum simulation, Schr¨odingerization

8.

Quantum algorithms for Young measures -- applications to nonlinear partial differential equations

Number of pages: 40 Posted: 08 Jun 2026
affiliation not provided to SSRN, affiliation not provided to SSRN, Nanjing University of Aeronautics and Astronautics and Johannes Gutenberg University Mainz
Downloads 5

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