In the HHL algorithm, phase estimation operator coherence depends only on input decomposition coefficients beta_i, while inverse phase estimation coherence depends on beta_i, matrix eigenvalues, and success probability P_s, decreasing as P_s increases for alpha in (1,2].
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Coherence dynamics in quantum algorithm for linear systems of equations
In the HHL algorithm, phase estimation operator coherence depends only on input decomposition coefficients beta_i, while inverse phase estimation coherence depends on beta_i, matrix eigenvalues, and success probability P_s, decreasing as P_s increases for alpha in (1,2].