Mirror Inverse Operations in Linear Nearest Neighbors Using Dynamic Learning Algorithm

We propose a new method to implement mirror inverse gate operations in 1-D linear nearest neighbor (LNN) array coupled through diagonal interactions, using a dynamic learning algorithm. This is accomplished by training a quantum system using a backpropagation technique, to find the parameters of the system Hamiltonian that implement the mirror inverse operation. We show how the training algorithm can be used as a tool for finding the parameters for implementing mirror inverse operations in LNN systems with increasing number of qubits. The key feature of our scheme is that once we find the system parameters using the learning algorithm, mirror inversion (MI) is accomplished simply by tuning the system parameters to these values and allowing the system to evolve for a chosen time interval. To validate our scheme, we compare our results against known results for an LNN system coupled through XY interactions. We also show how the scheme can be used to implement MI operations in the presence of unwanted couplings.