ABSTRACT
The central issue in applications of quantum information processing [1-3] is
the realisation of scalable quantum bits (qubits) and gates. The spins of in-
dividual electrons localized in semiconductor nanostructures are considered
as viable candidates for qubits due to their quantum two-level nature and
measured long spin coherence times [4-6]. In this design, the states |0〉 and |1〉 of the qubit are identified as the spin down and up states of the electron spin, respectively, and an array of N localized interacting spins forms
the quantum register [7, 8]. Quantum computation with such a quantum
register involves a coherent time evolution of its state, driven by a sequence
of quantum operations. Since the single-and two-qubit operations form a
minimal set sufficient to implement any quantum algorithm [3], the quan-
tum computer can be modeled by the Heisenberg Hamiltonian:
Hˆ = µB ~
gi ~Bi ~Si + 1
~SiJij ~Sj . (1.1)
Here µB is the Bohr magneton, gi and ~Bi are, respectively, the local Lande´
factor and the local magnetic field in the vicinity of the spin ~Si, and Jij is
the pairwise exchange coupling between the ith and jth spins. As described
by the first term in the above Hamiltonian, the single-qubit rotations are
performed by coupling each spin to an external magnetic field. In this
approach the individual qubits are addressed either by using local magnetic
fields, or by tuning the Lande´ factor gi of each spin separately. On the
other hand, the two-qubit operations are implemented by controlling the
exchange interactions Jij between pairs of spins [8, 9].
