Transferência de estados quânticos em cadeias de spins desordenadas: cadeira com aperiodicidade e linha de grafeno

Abstract

Quantum computing is already a reality today. Although the question about the types of tasks that a quantum computer must solve is still (to a large extent) open, many are the potentialities already observed, and it is expected that, in the near future, the use of this new tool will enable researchers to make new discoveries beyond imagination and current reach. However, like any emerging technology the quantum computer faces a series of obstacles that prevent its further production and diffusion. Of these obstacles, we can highlight as one of the main the transfer of information, mainly when dealing with short distances (i.e. between internal devices of the machine). As a solution, the idea of using spin chains for state transfer was proposed by Bose at the beginning of this century, originating a series of other studies investigating the benefits of use and conditions of state transfer by spin chains, seeking improve the protocol as possible. It is worth mention the work of Wójcik et al., who developed the method of transferring quantum states between two spins by loosely coupling them to the ends of the network. This thesis is formed by two theoretical studies, in which the viability of some spin channels for carrying out the transfer of quantum states was verified. First, we studied the effectiveness of a one-dimensional spin chain whose sites are under the effect of serial magnetic fields that follow the aperiodicity proposed by S. Das Sarma in the late 1980s. We show that the transfer can occur with high values of fidelity, as long as the onsite energy of the sending (receiving) spins are tuned in the spectrum region of the aperiodic chain that allows the existence of extended states along the chain. The tradeoff between the speed and fidelity of the transfer shows that the efficiency is comparable with a homogeneous chain. In the second study, quantum states are transferred using a quasi-one-dimensional chain that simulates graphene. Our results point to the transfer with high fidelity and high sensitivity to the static fluctuation of the energies of interaction between the spins. This sensitivity can be explained by spectral analysis of the chain, revealing the existence of localized modes that prevent effective transmission. In both cases, the Wójcik et al. protocol was used. Given that it has the capacity to create maximally entangled states between the sending and receiving spins, measures of concurrence between them were also taken, also demonstrating the creation of Bell states.