Decoherence of an exchange qubit by hyperfine interaction

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.Comment: 15 pages, 8 figure

Optimizing electrically controlled echo sequences for the exchange-only qubit

“…The qubit subspace of the exchange-only qubit is the two-dimensional space characterized by the total spin s = 1/2 and the spin in quantization (z) direction s z = 1/2, see [1]. Therefore, leakage is possible to the state with s = 3/2 and s z = 1/2 in the presence of a magnetic field gradient in z-direction [4]. In this work we assume that the exchange coupling is only switched of for the negligibly short time of an echo pulse and the dephasing in the Overhauser field happens for J 12 = J 23 = 0.…”

“…For the degenerate exchange-only qubit, the situation is more complicated due to the existence of a leakage state [5]. Applying spin-echo techniques to each spin individually is not favorable as this requires magnetic control which contradicts the concept of exchange-only quantum computing [4]. West and Fong [6] introduced an echo scheme for the exchange-only qubit which is based on SWAP operations between neighboring spin states.…”

Characterizing gate operations near the sweet spot of an exchange-only qubit

“…For GaAs-based devices, most leakage channels can be suppressed by enforcing sizeable energy splittings. 15 As consistent with recent experiments, 13 we therefore consider the energy hierarchy gµ B B J gµ B ∆B > 0, where J is the exchange interaction generated by the tunnel couplings. (In Appendix F, we also consider 28 Si-based devices, which do not require such an energy heirarchy, due to the absence of nuclear spins.)…”

“…18,19 In Ref. 15, we provided a detailed account of magnetic noise from the Overhauser fields of nuclear spins on the decoherence of an exchange-only qubit. Here, we simulate realistic gate operations including quasistatic random Overhauser fields 20 and charge noise.…”

“…However, in practice it may be necessary to turn on the exchange interactions and magnetic field at all times, to suppress leakage into the non-logical sector of the Hilbert space. 14,15 The exchange-only qubit provides an ideal platform for assessing the effect of sweet spots, since all gate operations are generated by the same physical process (the exchange interaction). 5,16,17 The only difference between X and Z-rotations is their proximity to the sweet spot.…”