A Mach-Zehnder interferometer (MZI) is provided to receive a coherent input photon in an initial pointer state for producing a continuously variable “faux qubit” in a magic state. The MZI apparatus includes first and second ports, first and second beam-splitters, first and second mirrors, and a modular interaction operator. The emitter produces an input coherent photon in an initial pointer state along an emission direction. The first and second ports are respectively disposed parallel and perpendicular to the emission direction. The first and second beam-splitters are disposed respectively collinearly with the emission direction and between the first and second ports parallel to and offset from the emission direction. The first and second mirrors are disposed respectively offset from and collinearly with the emission direction. The modular interaction operator is disposed between the first mirror and the second beam-splitter for measuring interaction therebetween to generate a post-selected magic state photon.