Transferência de estados quânticos e emaranhamento de formação em cadeias e grafos de spin-1/2

Abstract

In this work, we present a bibliographic review of spin-1/2 chains in the context of Quantum Computing and Quantum Information, highlighting their applications and possible experimental implementations. We discuss topics such as the generation and storage of bipartite entanglement between sites of spin chains. Additionally, we investigate and exemplify the dynamics of quantum state transfer in these chains. The Hilbert space describing the quantum state of a chain composed of N coupled spins has a dimension of 2N. However, when studying state transfer, a simplified approach based on graph theory can be adopted, in which the Hilbert space dimension scales linearly with N, provided the chain exhibits only a single excitation. This is because, in this case, the relevant subspace of the Hamiltonian can be equivalently represented by the adjacency matrix of a graph associated with the chain. This equivalence simplifies calculations, such as fidelity in state transfer, making them computationally more efficient. Based on this approach, we present results on state transfer in spin chains, as well as alternative configurations for generating and storing entanglement in decoupled chains.