Quantum logic gates for spin cluster qubits

Abstract

We study the low energy states of one-dimensional spin chain clusters consisting of three spin-1/2 Heisenberg particles. When applying an external magnetic field on the spin chain cluster, the ground state doublet will generate Zeeman splitting. As a two-level quantum system, the split ground state doublet can be defined as a new ‘spin cluster qubit’. The cluster quibit is shown to be more robust with a smaller decoherence rate. We realize universal single-qubit gates with the algebraic dynamical method, by applying a time-dependent magnetic field on the spin cluster. We also investigate a two-qubit system made up of two such Heisenberg spin chain clusters which interact through a tunable Heisenberg coupling. In the two-qubit product basis, the controlled quantum phase gates can be generated by applying a magnetic field along the z-axis on the system of the two clusters. One can realize the controlled-NOT gate through a three-step time evolution by adjusting the corresponding physical parameters. Our scheme involves two kinds of dynamically distinct operations, which is much simpler and more feasible.