Starting from standpoint of a model of the brain based on superluminal tunneling photons, the author has described theoretically the possibility of a brain-like computer that would be more powerful than Turing machines, and that would allow non-Turing computation. It may hold the key to clarify the origin of human consciousness itself. According to the brain model proposed, which is based on superluminal particles, it has been shown that microtubles in the biological brain have the possibility to achieve large quantum bit computation at room temperature which is superior in performance to conventional processors.