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). Specifically, 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.
We study a quantum transverse Ising model with p-spin interactions in the presence of a random field. The formulation for the free energy of the system is derived by making use of the Suzuki–Trotter approach with the thermodynamic perturbation theory, and the first-order transitions are obtained in the limit p → ∞.
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