A method includes receiving a representation of an N-mode interferometer and a representation of at least one imperfection associated with the N-mode interferometer at a processor, N being a positive integer value. The processor identifies multiple two-mode interferometers and multiple phases based on the representation of the N-mode interferometer and the representation of the at least one imperfection. The multiple two-mode interferometers and the multiple phases are configured to apply a unitary transformation to an input signal. The method also includes sending a signal to cause at least one of storage or display of a representation of the multiple two-mode interferometers and a representation of the multiple phases.