Decoherence of an exchange qubit by hyperfine interaction

TL;DR

This paper investigates the decoherence mechanisms of a three-electron-spin qubit in a semiconductor triple quantum dot, analyzing inhomogeneous and homogeneous dephasing, and providing estimates for various decoherence times relevant for quantum information processing.

Contribution

It develops an effective pure dephasing Hamiltonian for a three-spin qubit, accounting for exchange interactions and hyperfine effects, and compares decoherence times to single-spin qubits.

Findings

Dephasing times are comparable to single-spin qubits.

Effective Hamiltonians accurately describe decoherence dynamics.

Hyperfine interaction impacts decoherence in triple quantum dots.

Abstract

We study three-electron-spin decoherence in a semiconductor triple quantum dot with a linear geometry. The three electron spins are coupled by exchange interactions J_{12} and J_{23}, and we clarify inhomogeneous and homogeneous dephasing dynamics for a logical qubit encoded in the (S=1/2,S_{z} =1/2) subspace. We first justify that qubit leakage via the fluctuating Overhauser field can be effectively suppressed by sufficiently large Zeeman and exchange splittings. For J_{12}=J_{23} and the case of J_{12} and J_{23} being different, we construct an effective pure dephasing Hamiltonian with the Zeeman splitting much larger than the exchange splitting. Both effective Hamiltonians have the same order of magnitude as that for a single-spin qubit, and the relevant dephasing time scales are of the same order as those for a single spin. We provide estimates of the dynamics of three-spin free induction decay, the decay of a Hahn spin echo, and the decay of echoes from a CPMG pulse sequence for GaAs quantum dots.