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Area of Science:

  • Computational Physics
  • Quantum Computing
  • Numerical Analysis

Background:

  • Numerical solutions for partial differential equations (PDEs) are crucial in computational physics.
  • Traditional methods struggle with the high time complexity of high-dimensional problems.
  • Quantum-based methods offer potential for solving complex PDEs.

Purpose of the Study:

  • To present a fast hybrid classical-quantum paradigm to accelerate solving PDEs.
  • To reduce the complexity of high-dimensional PDE solutions.
  • To leverage quantum computing for efficient numerical solutions.

Main Methods:

  • Discretization of PDEs into systems of linear equations.
  • Application of the block successive over-relaxation (SOR) method to manage qubit limitations.
  • Iterative block-wise solving of subsystems on Advantage quantum computers.
  • Combining subsystem solutions to achieve the overall PDE solution.

Main Results:

  • The proposed hybrid method accelerates the solution of high-dimensional PDEs.
  • The method achieves up to a 2x speedup compared to existing methods.
  • Effective utilization of a limited number of qubits for complex problem-solving.

Conclusions:

  • The hybrid classical-quantum SOR paradigm offers a significant acceleration for solving PDEs.
  • This approach demonstrates the practical application of quantum computing in computational physics.
  • The block SOR method effectively addresses qubit constraints in quantum PDE solvers.