Suppression of hyperfine dephasing by spatial exchange of double quantum dots

We examine the logical qubit system of a pair of electron spins in double quantum dots. Each electron experiences a different hyperfine interaction with the local nuclei of the lattice, leading to a relative phase difference, and thus decoherence. Methods such as nuclei polarization, state narrowing, and spin-echo pulses have been proposed to delay decoherence. Instead we propose to suppress hyperfine dephasing by the adiabatic rotation of the dots in real space, leading to the same average hyperfine interaction. We show that the additional effects due to the motion in the presence of spin-orbit coupling are still smaller than the hyperfine interaction, and result in an infidelity below ${10}^{-4}$ after ten decoupling cycles. We discuss a possible experimental setup and physical constraints for this proposal.

Figure 1

Suggested electrode geometry for a rotating double-quantum-dot qubit with top and bottom gates in different shades of gray. Exchange gates via real space rotation, as opposed to tunneling, are expected to strongly reduce the qubit sensitivity to charge noise.

Figure 2

Time-dependent adiabatic trajectories used in the simulations. Plotted is the position of the first dot parametrized in terms of the angle $\theta$ as a function of time $t$. The angle-dependent positions were defined as a sum of properly scaled and shifted hyperbolic tangents. Single direction rotations suppress the effect of a static Overhauser field but not of a time-varying one. Longer rotation sequences like alternating forward-and-back suppress the effect of a linear in time Overhauser field. Arbitrary rotations on the Bloch sphere may be accomplished using additional operations when the dot is stationary, corresponding to the flat segments in the sequence.

Figure 3

Simulated qubit infidelity $1-\langle F\rangle$ [Eq. (35)] in the vicinity of the first full rotation period of the double-dot qubit at $t=T$. Position-dependent magnetic field $B_{\mu }\left(\theta \right)$ is assumed static, and the rotation period $T$ is chosen commensurate with the Larmor frequency ${\omega }_{0}T/2\pi =400$. Dashed line: Only $B_z\left(\theta \right)$ is included; the infidelity minimum is exactly at $t=T$, in agreement with Eq. (54) which is exact in this situation. Dotted line: Only the transverse components $B_{\mu }\left(\theta \right)$, $\mu =x,y$ are included. The infidelity minimum is slightly off the commensurate time $t=T$ due to the terms not included in Eq. (52). All three components of the field $B_{\mu }\left(\theta \right)$ are included for the red solid line.

Figure 4

Simulation results for fidelity measured at the end of each cycle, for a linear time dependence of $B_{1i}^{\mu }$ with (a) forward, (b) forward-back dot rotations (cf. Fig. 2), as well as (c) forward-back for quadratic time dependence.