Non-local universal gates generated within a resonant magnetic cavity

Abstract

Quantum Information is a quantum resource being advised as a useful tool to set up information processing. Despite physical components being considered are normally two-level systems, still the combination of some of them together with their entangling interactions (another key property in the quantum information processing) become in a complex dynamics needing be addressed and modeled under precise control to set programmed quantum processing tasks. Universal quantum gates are simple controlled evolutions resembling some classical computation gates. Despite their simple forms, not always become easy fit the quantum evolution to them. SU(2) decomposition is a mechanism to reduce the dynamics on SU(2) operations in composed quantum processing systems. It lets an easier control of evolution into the structure required by those gates by the adequate election of the basis for the computation grammar. In this arena, SU(2) decomposition has been studied under piecewise magnetic field pulses. Despite, it is completely applicable for time-dependent pulses, which are more affordable technologically, could be continuous and then possibly free of resonant effects. In this work, we combine the SU(2) reduction with linear and quadratic numerical approaches in the solving of time-dependent Schr\"odinger equation to model and to solve the controlled dynamics for two-qubits, the basic block for composite quantum systems being analyzed under the SU(2) reduction. A comparative benchmark of both approaches is presented together with some useful outcomes for the dynamics in the context of quantum information processing operations.