  We propose to implement quantum computing based on electronic spin qubits by
controlling the propagation of the electron wave packets through the helical
edge states of quantum spin Hall systems (QSHs). Specfically, two
non-commutative single-qubit gates, which rotate a qubit around z and y axes,
can be realized by utilizing gate voltages either on a single QSH edge channel
or on a quantum point contact structure. The more challenging two-qubit
controlled phase gate can be implemented through the on-demand capacitive
Coulomb interaction between two adjacent edge channels from two parallel QSHs.
As a result, a universal set of quantum gates can be achieved in an
all-electrical way. The fidelity and purity of the two-qubit gate are
calculated with both time delay and finite width of the wave packets taken into
consideration, which can reach high values with the existing high-quality
single electron source.
