A Quantum Dot Neural Network

We present a mathematical implementation of a quantum mechanical artificial neural network, in the quasi-continuu m regime, using the nonlinearity inherent in the real-time propagation of a quantum system coupled to its environment. Our model is that of a quantum dot molecule coupled to the substrate lattice through optical phonons, and subject to a timevarying external field. Using discretized Feynman path integrals, we find that the real time evolution of the system can be put into a form which resembles the equations for the virtual neuron activation levels of an artificial neural network. The timeline discretization points serve as virtual neurons. We then train the network using a simple gradient descent algorithm, and find it is possible in some regions of the phase space to perform any desired classical logic gate. Because the network is quantum mechanical we can also train purely quantum gates such as a phase shift.