Harrow–Hassidim–Lloyd Algorithm

The HHL algorithm (Harrow–Hassidim–Lloyd) is a quantum algorithm for solving systems of linear equations exponentially faster than the best known classical methods, under certain conditions. It encodes the solution vector as a quantum state using phase estimation and controlled rotations based on the eigenvalues of . However, it only provides a quantum state proportional to , not its classical components, and its speedup depends on properties like sparsity and condition number of .