Probabilistic quantum algorithm prepares mixed states proportional to Lyapunov equation solutions and matrix inverses using oracles for input matrices and a deterministic stopping rule.
Equation (B19) has a unique solution if and only if the eigenvalues of A satisfy λi + λ∗ j ̸= 0 for all λi, λj ∈ λ(A)
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Probabilistic quantum algorithm for Lyapunov equations and matrix inversion
Probabilistic quantum algorithm prepares mixed states proportional to Lyapunov equation solutions and matrix inverses using oracles for input matrices and a deterministic stopping rule.