Optical processing of optical labels is expected for increasing processing speed in network routers. We previously proposed optical waveguide circuits for recognition of optical QAM codes by detecting a null output port. The circuits are based on a recognition circuit for QPSK codes. In the device, however, optical or electrical inverters with large dynamic range are required. In this paper, we propose optical circuits to recognize optical QAM codes by maximum output with a post-processor consisting of thresholders and logical circuits. The recognition function of the waveguide circuit is numerically proved by FD BPM.