Quantum State Transfer in Spin Chains

ANALIA ZWICK

FaMAF - Serie D

Año: 2012 p. 131

0-8436-1072-7

Quantum information processing has been extensively studied during the past years. One of the main challenges of actual physical implementations has been the manipulation of the quantum information with sufficient accuracy to prevent errors. In particular it is important to be able to transfer quantum information between different elements of a quantum computer. In this respect, spin chain systems have been proposed as quantum channels for the transmission of quantum states, where the spins- 12 act as the quantum bits. From this proposal, these systems have been studied to improve their performance for the transmission of states. One of the main goals is to find systems where states can be transferred without any control during the transfer procedure or with only minimal control requirements to thereby prevent the introduction of errors. But even in these systems, static perturbations, due to imperfections in the manufacture of the channel, modify the interactions between the spins. Furthermore, the interaction with the environment can also degrade the quality of the transfer. That is why we consider that a complete characterization of the reliability and robustness of these quantum channels should take into account the action of such perturbations, present in a possible implementation. This is the research topic of this thesis. First, we introduce the basic ideas about quantum information and the necessary elements to achieve and to characterize the transfer of spin states in chains. Then we study the properties of boundary-controlled unmodulated spin chains and we determinate the optimal conditions to transfer a quantum state quickly and with high fidelity. Afterwards, we study spin chains where each coupling, has been specifically designed to achieve a perfect transmission. We consider these systems under the influence of static disorder and we de- termine the properties that make them robust for the transfer. Finally, we compare these two classes of qubit chains, boundary-controlled and fully engineered spin chains, against different models of static disorder and we determine under which conditions they are most robust for state transfer.