sf.decompositions.rectangular_compact

rectangular_compact(U, rtol=1e-12, atol=1e-12)

Rectangular decomposition of a unitary with sMZIs and phase-shifters, as given in FIG. 3+4 and “The Clements Scheme” section of (arXiv:2104.0756).

Parameters

U (array) – unitary matrix

Returns

A dictionary containing the following items:

• m: the length of the matrix

• phi_ins: parameter of the phase-shifter at the beginning of the mode

• sigmas: parameter of the sMZI \(\frac{(\theta_1+\theta_2)}{2}\), where \(\theta_{1,2}\) are the values of the two internal phase-shifts of sMZI

• deltas: parameter of the sMZI \(\frac{(\theta_1-\theta_2)}{2}\), where \(\theta_{1,2}\) are the values of the two internal phase-shifts of sMZI

• phi_edges: parameters of the edge phase shifters

• phi_outs: parameter of the phase-shifter at the end of the mode

Return type

dict

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