unitaria.Pseudoinverse

class unitaria.Pseudoinverse(A: Node, condition: float, tolerance: float, guaranteed: bool = False)[source]

Bases: ProxyNode

This node implements the Moore-Penrose pseudoinverse of A with the given tolerance, if condition is the ratio between A.normalization and A s smallest singular value.

Implements Theorem 41 from https://arxiv.org/abs/1806.01838

Parameters:

  • A – The node to be inverted

  • condition – An upper bound on the inverse of nonzero singular values of A. This is the same as the usual definition of the condition of a matrix iff the largest singular value is its normalization, i.e. if the block-encoding has optimal subnormalization.

  • tolerance – The absolute error tolerance

  • guaranteed – Determines if the accuracy should be guaranteed using analytical bounds (ignoring numerical errors). If this is set to false, this function will use a heuristic which will result in polynomials of lower degrees while usually still providing the requested precision.