# 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