sf.decompositions.covmat_to_hamil

covmat_to_hamil(V, tol=1e-10)[source]

Converts a covariance matrix to a Hamiltonian.

Given a covariance matrix V of a Gaussian state \(\rho\) in the xp ordering, finds a positive matrix \(H\) such that

\[\rho = \exp(-Q^T H Q/2)/Z\]

where \(Q = (x_1,\dots,x_n,p_1,\dots,p_n)\) are the canonical operators, and Z is the partition function.

For more details, see https://arxiv.org/abs/1507.01941

Parameters
  • V (array) – Gaussian covariance matrix

  • tol (int) – the number of decimal places to use when determining if the matrix is symmetric

Returns

positive definite Hamiltonian matrix

Return type

array