Exchange interaction of hole-spin qubits in double quantum dots in highly anisotropic semiconductors

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 √ SWAP gate. Furthermore, we show that the anisotropyinduced spin-orbit effects can be comparable to that of the direct Rashba spin-orbit interaction for experimentally feasible electric field strengths.

Squeezed hole spin qubits in Ge quantum dots with ultrafast gates at low power

“…2b). The optimal SOI saturates to v * = 2.56 2 /ml E ≈ 25 meV nm×E 1/3 when w 3l E ≈ 24 nm×E −1/3 ; this condition is easily met in state-of-the-art devices, where w ∈ [15,30] nm and E 1 V/µm [1]. We remark that the case w l E also describes inversion layers.…”

“…acting on the Kramer partners | ↑ and | ↓ . Here, we introduce a matrix gij = δ ij (α i − β i p 2 y / 2 ) of wire gfactors, which is diagonal because of symmetry [27,30] and includes momentum dependent corrections β i [14,15]. The orbital gap ωy differs from the frequency ω y because of the effective mass m, i.e.…”

Hole Spin Qubits in Ge Nanowire Quantum Dots: Interplay of Orbital Magnetic Field, Strain, and Growth Direction

“…Generally, there are further terms possible, such as a diagonal term linear in k y or an off-diagonal term quadratic in k y . However, these terms are zero in the isotropic LK Hamiltonian [52]. This effective model works well in different geometries, however in this section we restrict ourselves to the analysis of NWs with square cross-section.…”

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits

“…A similar route has recently been used to investigate the dynamics of a pair [ 25 , 26 , 27 , 28 , 29 , 30 , 31 ] or a chain [ 32 , 33 ] of coupled spins (also greater than ) subjected to time-independent and time-dependent [ 34 , 35 , 36 ] external magnetic fields. Symmetry arguments have also been exploited to elegantly bring to light intriguing dynamic features of physical systems living in Hilbert spaces of infinite dimensions [ 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 ]. In Section 4 it is demonstrated that the time evolution of the two dipolarly coupled spins nests a qutrit subdynamics governed by a Hamiltonian model that is explicitly derived.…”