Abstract
We study the exchange interaction between two hole-spin qubits in a double quantum dot setup in a silicon nanowire in the presence of magnetic and electric fields. Based on symmetry arguments we show that there exists an effective spin that is conserved even in highly anisotropic semiconductors, provided that the system has a twofold symmetry with respect to the direction of the applied magnetic field. This finding facilitates the definition of qubit basis states and simplifies the form of exchange interaction for two-qubit gates in coupled quantum dots. If the magnetic field is applied along a generic direction, cubic anisotropy terms act as an effective spin-orbit interaction introducing novel exchange couplings even for an inversion symmetric setup. Considering the example of a silicon nanowire double dot, we present the relative strength of these anisotropic exchange interaction terms and calculate the fidelity of the $\sqrt{\text{SWAP}}$ gate. Furthermore, we show that the anisotropy-induced spin-orbit effects can be comparable to that of the direct Rashba spin-orbit interaction for experimentally feasible electric field strengths.
Highlights
Over the last two decades localized spins in quantum dots (QDs) became a promising candidate for scalable quantum computing [1,2]
Holes confined in quantum dots [13,14] have recently attracted much attention due to the possibility of fast singlequbit control by virtue of a strong spin-orbit interaction (SOI) [15,16,17,18,19,20,21] and slow decoherence owing to the suppressed hyperfine interaction [19,22,23,24,25]
VI we propose a symmetry-decomposition of the Hamiltonian that reveals the different effective spin mixing terms, compare the spin mixing effect of the cubic anisotropy and the direct Rashba SOI (DRSOI), present the relative energy scales of the anisotropic corrections to the exchange i√nteraction, and calculate the anisotropylimited fidelities of a SWAP gate
Summary
Over the last two decades localized spins in quantum dots (QDs) became a promising candidate for scalable quantum computing [1,2]. One of our central results is shown, where we present the effect of the hitherto neglected anisotropy-induced spin mixing mechanism on the exchange interaction Jand the induced Zeeman splittings This mixing will lead to anisotropic corrections to the exchange interaction even in the presence of inversion symmetry.
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