Probabilistic quantum algorithm prepares mixed states proportional to Lyapunov equation solutions and matrix inverses using oracles for input matrices and a deterministic stopping rule.
The diamond norm of a linear map A : Cd×d → Cd×d is defined as ∥A∥⋄ = max {∥(A ⊗ Id)(X)∥1 | X ∈ C2d×2d, ∥X∥1 ≤ 1}
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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.