Effect of electron-nuclear spin interactions for electron-spin qubits localized in InGaAs self-assembled quantum dots

Abstract

Lee, Seungwon; von Allmen, Paul; Oyafuso, Fabiano; and Klimeck, Gerhard, "Effect of electron-nuclear spin interactions for electronspin qubits localized in InGaAs self-assembled quantum dots" (2005 The effect of electron-nuclear spin interactions on qubit operations is investigated for a qubit represented by the spin of an electron localized in an InGaAs self-assembled quantum dot. The localized electron wave function is evaluated within the atomistic tight-binding model. The electron Zeeman splitting induced by the electron-nuclear spin interaction is estimated in the presence of an inhomogeneous environment characterized by a random nuclear spin configuration, by the dot-size distribution, alloy disorder, and interface disorder. Due to these inhomogeneities, the electron Zeeman splitting varies from one qubit to another by the order of 10 −6 , 10 −6 , 10 −7 , and 10 −9 eV, respectively. Such fluctuations cause errors in exchange operations due to the inequality of the Zeeman splitting between two qubits. However, the error can be made lower than the quantum error threshold if an exchange energy larger than 10 −4 eV is used for the operation. This result shows that the electron-nuclear spin interaction does not hinder quantum-dot based quantum computer architectures from being scalable even in the presence of inhomogeneous environments.

Spin decoherence from Hamiltonian dynamics in quantum dots

“…Using the known experimental decay time scales of order 10-100 nanoseconds, and estimating the number of nuclei interacting with the qubit to be, N ∼ 100 (see Section II), the typical effective coupling strength relavant for QDQC systems works out to be, K ∼ 10 −8 eV. These results are in broad agreement with the results obtained by [27]. This agreement justifies writing an effective Heisenberg interaction of the qubit with the total bath spin.…”

“…The ef-fective coupling to the nuclear spins which are farther is accordingly suppressed, with the maximum contribution coming from the nearest nuclei, all of which are roughly equidistant from the electron. Indeed, in GaAs there are about 45 nuclei in a volume of 1 nm 3 , and the electron wave function is roughly uniform over a distance of 2-3 nm (while the size of the quantum dot is about 20 nm) [17,27]. This translates into about a few hundred nuclei that interact with the qubit with the same coupling strength K i in Eq.1, and thus the Hamiltonian assumes a simple form…”

Donor hyperfine Stark shift and the role of central-cell corrections in tight-binding theory

“…Therefore it is fundamentally not possible to quantitatively determine the value of the hyerperfine coupling A(0) as is possible from the ab-initio type calculations [19]. Nevertheless, we apply the methodology published by Lee et al [37] to estimate the value of |ψ(r 0 )| 2 from our model, where we have used the value of bulk Si conduction electron at the nuclear site as ≈ 9.07 × 10 24 cm −3 [38,39] and the value of the atomic orbital ratio φ s * (0)/φ s (0) computed to be 0.058 from the assumption of the hydrogen-like atomic orbitals with an effective nuclear charge [40]. We believe that this provides a good qualitative comparison of A(0) ∝ |ψ(r 0 )| 2 from our model with the experimental value, and along with the quantitative match of the donor binding energies (A 1 , T 2 , and E) and the Stark shift of hyerfine (η 2 ), serve as a benchmark to evaluate the role of the central-cell corrections in the tight-binding theory.…”

Quantum measurement of a mesoscopic spin ensemble

“…This implies that the electron experiences an effective magnetic field (Overhauser field, B nuc ) with large variance, reducing the fidelity of quantum memory and quantum gates. This reduction arises both from the inhomogeneous nature of the field ( B nuc varies from dot to dot) [29] and the variation of B nuc over time due to nuclear-spin dynamics (even a single electron experiences different field strengths over time, implying loss of fidelity due to time-ensemble averaging).…”