Finding analytical solution for mirror inverse gate operations in quantum systems with diagonal interactions

Abstract

We present an analytical solution for implementing mirror inverse (MI) gate operations directly in quantum systems with diagonal Ising interactions. To achieve this, we use a dynamic learning algorithm as a tool for finding parameters of the system Hamiltonian that realizes the desired MI gate operation directly in systems with fewer qubits. By carefully analyzing the parameter values obtained in these systems, we find analytical solutions that can be extended to calculate parameter values to achieve MI gate operations in systems with larger numbers of qubits without the need for training.