Human-Brain Artificial-Intelligence Matrix is a new technology aims to connect the human brain with the machine for the purpose of enabling the human brain to perform defined functions even if it becomes unable to perform them such as performing the function of vision in case of blindness, the function of hearing in case of deafness, Performing the function of motion in case of paralysis and many other functions. This technology will be based on the Cognition Theory which I argue about that the whole process of cognition can be treated quantum-mechanically. The cognition starts when a neuron sends data to be processed in the brain and ends in an effector to respond. The data “action potential” is a current of particles which can be described quantum-mechanically as a wave-impulse based on the dual nature of the particles. The neurons are a net of entangled cells classically and quantum-mechanically. When the action potential changes the potential of the neurons, it creates quantum mechanical potential wells and barriers. The action potential perfectly transmits in and out the neurons through quantum mechanical tunnels. The form of energy before processing is not the same after, but the amount of energy is always conserved. Since the neurons are entangled during the action potential transmission, the brain and effector will be entangled during the action potential processing. The effector’s cognition of data must be a discrete cognition of single-valued data from its self-adjoint matrix which entangled with brain matrix.