Quantum Simulataneous Recurrent Networks for Content Addressable Memory

Summary

We explore a model for a quantum Hopfield artificial neural network, in which qubits are prepared in an initial state and allowed to evolve to steady state. We derive the equations for finding their stable states, by minimizing the Lyapunov energy. We apply the equations first to the cytoskeleton of a biological neuron, where the qubits are microtubulins in a microtubule. Our method can reproduce classical calculations made earlier by Tuszynski et al., but because it is a fully quantum method can also explore the possibility that an artificial computing structure based on an array of tubulins can act as a quantum computer. We then derive a method for training the quantum network to converge to a stable target pattern, given an input pattern, and show that a spatial array of qubits can be trained to perform the CNOT, which with a rotation is a universal quantum gate. This means that a large enough array can in principle be trained to do any calculation.