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Quantum Linear Solvers for CFD matrices

This directory contains quantum linear solvers developed for computational fluid dynamics (CFD) applications. The solvers are designed to integrate with hybrid classical–quantum workflows, such as the segregated SIMPLE solver and the implicit coupled solver in the qc-cfd repository.

Solvers

  • Quantum Singular Value Transformation (QSVT) for matrix inversion
  • Linear Combination of Unitaries (LCU) of a Chebyshev polynomial approximation

The code provides two block-encoding implementations for the CFD matrices:

  • LCU for Pauli decomposition, using a Graycode approach
  • LCU for banded diagonals according to Lapworth & Sünderhauf

Notebooks

  1. verify_block_encoding.ipynb shows how to call and run the block-encoding qfunc for a given matrix.
  2. chebyshev_approximation.ipynb demonstrates how the Chebyshev approximation for the inversion function is define.
  3. qls_qsvt and qls_chebyshev_lcu, define the generic quantum solvers that can be plugged into the hybrid code.
  4. The main classical and quantum functions are implemented in separate Python modules for clarity and reuse.