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Quantum computing and preconditioners for hydrological linear systems.

John Golden1, Daniel O'Malley2, Hari Viswanathan2

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Quantum computing offers a solution for modeling complex hydrological fracture networks, overcoming classical limitations. A novel inverse Laplacian preconditioner significantly improves quantum linear system solvers for these challenging earth science problems.

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Area of Science:

  • Computational Earth Sciences
  • Quantum Computing
  • Hydrological Modeling

Background:

  • Modeling hydrological fracture networks is computationally intensive.
  • Classical computers struggle with the large linear systems required for accurate fracture system prediction.
  • Ill-conditioned systems pose a significant challenge for quantum linear system solvers.

Purpose of the Study:

  • To investigate quantum approaches for solving large linear systems in hydrological fracture modeling.
  • To address the challenge of ill-conditioned systems in quantum simulations.
  • To develop a novel preconditioner for quantum linear solvers.

Main Methods:

  • Tested existing quantum techniques for improving system condition numbers.
  • Introduced and analyzed the inverse Laplacian preconditioner.
  • Evaluated the quantum implementation of the proposed preconditioner.

Main Results:

  • Existing quantum techniques were insufficient for improving condition numbers.
  • The inverse Laplacian preconditioner improved system condition number scaling from O(N) to [Formula: see text].
  • The preconditioner admits a quantum implementation.

Conclusions:

  • The inverse Laplacian preconditioner is a critical advancement for quantum solvers in hydrological modeling.
  • This work paves the way for quantum solutions to complex earth science problems.
  • Demonstrates a novel real-world application for quantum linear systems algorithms.