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Electron-spin qubit operation error due to electron-nuclear spin interaction

Seungwon Lee, Paul von Allmen, Fabiano Oyafuso, Gerhard Klimeck, K. Birgitta Whaley

Published May 10, 2004• 0 citations
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Effects of electron-nuclear spin interaction on electron-spin qubit operations

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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 10−9eV, 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 10−4eV 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.

arXiv:quant-ph/0403122•Journal of Applied Physics•Jan 24, 2005•25 citations

Dipolar Coupling Errors in Nuclear Spin Qubits

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ABSTRACT Nuclear spins have been studied since the beginning of quantum information science since they form the prototypical qubit with long coherence times and high‐fidelity operation. To perform practical fault‐tolerant quantum computations, however, not only do we require precision manufacturing techniques to produce millions of qubits, but these techniques need to consistently yield low‐error qubits. A deep understanding and control of the interactions between the qubits and their environment are needed as we scale so that devices can be engineered to avoid high error rates. In this work, we experimentally and theoretically characterize two often‐overlooked error mechanisms affecting nuclear spin qubits in silicon caused by local interactions. The first is the direct magnetic interactions between nuclear spins, causing dipolar coupling errors, and the second is the interactions between the nuclear spins and their associated electron spin, causing “hotspots” of anisotropic hyperfine coupling errors. By modeling the properties of the combined electron–nuclear spin system as a function of magnetic field, contact hyperfine strength, and electron tunnel rate, we show how these errors can be reliably mitigated, giving rise to readout fidelities of .

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Nonideality of quantum operations with the electron spin of a 31P donor in a Si crystal due to interaction with a nuclear spin system

Semion K. Saikin, Leonid Evgenevich Fedichkin

We examine a ${}^{31}\mathrm{P}$ donor electron spin in a Si crystal to be used for the purpose of quantum computation. The interaction with an uncontrolled system of ${}^{29}\mathrm{Si}$ nuclear spins influences the electron-spin dynamics appreciably. The hyperfine field at the ${}^{29}\mathrm{Si}$ nuclei positions is noncollinear with the external magnetic field. Quantum operations with the electron wave function, i.e., using magnetic-field pulses or electrical gates, change the orientation of hyperfine field and disturb the nuclear-spin system. This disturbance produces a deviation of the electron spin qubit from an ideal state, at a short-time scale in comparison with the nuclear-spin diffusion time. For H${}_{\mathrm{ext}}\ensuremath{\approx}9$ T, the estimated error rate is comparable to the threshold value required by the quantum error correction algorithms. The rate is lower at higher external magnetic fields.

arXiv:cond-mat/0212501•Physical review. B, Condensed matter•Apr 28, 2003•25 citations
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 10−9eV, 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 10−4eV 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.
ABSTRACT Nuclear spins have been studied since the beginning of quantum information science since they form the prototypical qubit with long coherence times and high‐fidelity operation. To perform practical fault‐tolerant quantum computations, however, not only do we require precision manufacturing techniques to produce millions of qubits, but these techniques need to consistently yield low‐error qubits. A deep understanding and control of the interactions between the qubits and their environment are needed as we scale so that devices can be engineered to avoid high error rates. In this work, we experimentally and theoretically characterize two often‐overlooked error mechanisms affecting nuclear spin qubits in silicon caused by local interactions. The first is the direct magnetic interactions between nuclear spins, causing dipolar coupling errors, and the second is the interactions between the nuclear spins and their associated electron spin, causing “hotspots” of anisotropic hyperfine coupling errors. By modeling the properties of the combined electron–nuclear spin system as a function of magnetic field, contact hyperfine strength, and electron tunnel rate, we show how these errors can be reliably mitigated, giving rise to readout fidelities of .
We examine a 31P{}^{31}\mathrm{P}31P donor electron spin in a Si crystal to be used for the purpose of quantum computation. The interaction with an uncontrolled system of 29Si{}^{29}\mathrm{Si}29Si nuclear spins influences the electron-spin dynamics appreciably. The hyperfine field at the 29Si{}^{29}\mathrm{Si}29Si nuclei positions is noncollinear with the external magnetic field. Quantum operations with the electron wave function, i.e., using magnetic-field pulses or electrical gates, change the orientation of hyperfine field and disturb the nuclear-spin system. This disturbance produces a deviation of the electron spin qubit from an ideal state, at a short-time scale in comparison with the nuclear-spin diffusion time. For H${}_{\mathrm{ext}}\ensuremath{\approx}9$ T, the estimated error rate is comparable to the threshold value required by the quantum error correction algorithms. The rate is lower at higher external magnetic fields.