The Topological Basis Realization for Six Qubits and the Corresponding Heisenberg Spin − 1 2 $-\frac {1}{2}$ Chain Model

Abstract

In this paper, we construct a new set of orthonormal topological basis states for six qubits with the topological single loop d = 2. By acting on the subspace, we get a new five-dimensional (5D) reduced matrix. In addition, it is shown that the Heisenberg XXX spin- $\frac {1}{2}$ chain of six qubits can be constructed from the Temperley-Lieb algebra (TLA) generator, both the energy ground state and the spin singlet states of the system can be described by the set of topological basis states.