sf.decompositions.triangular

triangular(V, tol=1e-11)

Triangular decomposition of a unitary matrix due to Reck et al.

See [26] for more details and [23] for details on notation.

Parameters

• V (array[complex]) – unitary matrix of size n_size

• tol (float) – the tolerance used when checking if the matrix is unitary: \(|VV^\dagger-I| \leq\) tol

Returns

returns a tuple of the form (tlist,np.diag(localV), None)

where:

• tlist: list containing [n,m,theta,phi,n_size] of the T unitaries needed

• localV: Diagonal unitary applied at the beginning of circuit

Return type

tuple[array]

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