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arXiv:0902.4566 · Physical Review Letters

Qubit Protection in Nuclear-Spin Quantum Dot Memories

Z. Kurucz, Martin W. Sørensen, Jacob M. Taylor, Mikhail D. Lukin, Michael Fleischhauer

Published Jul 2, 2009• 48 citations
arXivHTMLPDF

Abstract

We present a mechanism to protect quantum information stored in an ensemble of nuclear spins in a semiconductor quantum dot. When the dot is charged the nuclei interact with the spin of the excess electron through the hyperfine coupling. If this coupling is made off-resonant, it leads to an energy gap between the collective storage states and all other states. We show that the energy gap protects the quantum memory from local spin-flip and spin-dephasing noise. Effects of nonperfect initial spin polarization and inhomogeneous hyperfine coupling are discussed.

DOI
10.1103/physrevlett.103.010502

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We present a mechanism to protect quantum information stored in an ensemble of nuclear spins in a semiconductor quantum dot. When the dot is charged the nuclei interact with the spin of the excess electron through the hyperfine coupling. If this coupling is made off-resonant, it leads to an energy gap between the collective storage states and all other states. We show that the energy gap protects the quantum memory from local spin-flip and spin-dephasing noise. Effects of nonperfect initial spin polarization and inhomogeneous hyperfine coupling are discussed.
Recently, an ensemble of nuclear spins in a quantum dot have been proposed as a long-lived quantum memory. A quantum state of an electron spin in the dot can be faithfully transfered into nuclear spins through controlled hyperfine coupling. Here we study the decoherence of this memory due to nuclear spin dipolar coupling and inhomogeneous hyperfine interaction during the storage period. We calculated the maximum fidelity of writing, storing, and reading operations. Our results show that nuclear spin dynamics can severely limit the performance of the proposed device for quantum information processing and storage based on nuclear spins.
Nuclear spins in quantum dots are promising candidates for fast and scalable quantum memory. By utilizing the hyperfine interaction between the central electron and its surrounding nuclei, quantum information can be transferred to the collective state of the nuclei and stored for a long time. However, nuclear spin fluctuations in a partially polarized nuclear bath degrade the quantum memory fidelity. Here, we introduce a noise-resistant protocol to realize fast and high-fidelity quantum memory through Hamiltonian engineering. With analytics and numerics, we show that a high-fidelity quantum state transfer between the electron and the nuclear spins is achievable at relatively low nuclear polarizations, due to the strong suppression of nuclear spin noises. For a realistic quantum dot with 104{10}^{4}104 nuclear spins, a fidelity surpassing 80% is possible at a polarization as low as 30%. Our approach reduces the demand for high nuclear polarization, making experimentally realizing quantum memory in quantum dots more feasible.
Schemes for the nuclear spin quantum memory are proposed based on a system composed of two electrons or one electron coupled to a single nuclear spin in isotopically purified group-IV elemental and II-VI compound semiconductors. The qubit consists of the singlet state and one of the triplet states of two electrons or simply of an electron spin. These systems are free from the decoherence due to the nuclear dipole-dipole interaction and are advantageous for the long memory time. In the case of two electrons, the protocol for the quantum state transfer between the electron-spin qubit and the nuclear spin qubit is based on the magnetic or electric field tuning of the singlet-triplet state crossing and on the hyperfine coupling supplemented with a well-defined scheme to initialize the nuclear spin. In the case of a single-electron qubit, the quantum state transfer is driven by the hyperfine interaction itself without the need of the nuclear spin initialization. Many practical systems are considered, e.g., two electrons loaded on a Si or ZnSe quantum dot, a single-electron charged state in a Si quantum dot doped with a P atom, a single-electron charged 28Si^{28}\text{S}\text{i}28Si quantum dot doped with an isotope atom of 29Si^{29}\text{S}\text{i}29Si, and a localized electron system of Si:P and ZnSe:F in the bulk crystal. General aspects of these systems are investigated and a comparison of merits and demerits is made between the two-electron qubit and the single-electron qubit.
The decoherence and fidelity of spin states in a localized single-electron quantum dot in the presence of a dc magnetic field, arising either from the nuclear hyperfine interaction within the dot or due to its coupling with another localized quantum dot, are examined in detail. A general framework for determining the time evolution of the reduced density matrix. for a single dot is presented, which is exact up to the second order in interaction with any reservoir. In particular, it is applied to the problem of nuclear hyperfine coupling, and approximate estimates of coherence decay time are made when the nuclear spins are either polarized or unpolarized and the internal dynamics of nuclear spins is determined mainly by the nuclear magnetic dipole-dipole interaction. The fidelity of a pure unperturbed electronic one-qubit spin state is obtained as a function of time, which is exact even on a very short timescale of logic gate operations. The time variation of the fidelity of the same one-qubit state on the localized dot as a part of the direct product with another one-qubit state on another localized dot arising because of coupling between these quantum dots is also calculated in this paper. In this case, we include both the single-particle tunnelling between the dots as well as the direct and exchange Coulomb interactions, including on-site Coulomb repulsion. This allows for the double occupation of a single dot. It is found that the loss of fidelity of such two-qubit states due to double occupancy and additional phase errors in the presence of appreciable dot-dot coupling can become a more severe limiting factor than that due to the hyperfine interaction in individual dots.
States with long coherence are a crucial requirement for qubits and quantum memories. Nuclear spins in epitaxial GaAs/AlGaAs quantum dots are a great candidate, offering excellent isolation from external environments and on-demand coupling to optical flying qubits. However, coherence times are limited to ≲ 1 ms by the dipole-dipole interactions between the nuclei and by the nuclear quadrupolar coupling to inhomogeneous crystal strain. Here, we combine strain engineering of the nuclear spin ensemble and tailored dynamical decoupling sequences to achieve nuclear spin coherence times exceeding 100 ms. Recently, a reversible transfer of quantum information into nuclear spin ensembles has been demonstrated in quantum dots: our results provide a path to develop this concept into a functioning solid-state quantum memory suitable for quantum repeaters in optical quantum communication networks.
In this thesis we present protocols for the polarization of nuclear spins in a quantum dot via the hyperfine interaction with a conduction band electron and give a quantitative solution to the master equation we derive. The collective interference effects limiting the polarization are studied in detail, and ways of mitigating them are proposed. At high polarization levels the electron-nuclear interaction is approximated with simple and practical (quantum optical) models, suggesting the possibility of novel coherent manipulation schemes which actively make use of the nuclei. Finally we demonstrate that even completely mixed nuclear spin ensembles can be utilized for the important task of sequentially generating entanglement between electron spins.