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arXiv:cond-mat/0605081 · Nanotechnology

Cross-talk compensation of hyperfine control in donor-qubit architectures

G Kandasamy, Cameron J. Wellard, Lloyd C. L. Hollenberg

Published Aug 22, 2006• 10 citations
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Abstract

We theoretically investigate cross-talk in hyperfine gate control of donor-qubit quantum computer architectures, in particular the Kane proposal. By solving the Poisson and Schrödinger equations numerically for the gated donor system, we calculate the change in hyperfine coupling and thus the error in spin-rotation for the donor nuclear-electron spin system, as the gate-donor distance is varied. We thus determine the effect of cross-talk-the inadvertent effect on non-target neighbouring qubits-which occurs due to closeness of the control gates (20-30 nm). The use of compensation protocols is investigated, whereby the extent of cross-talk is limited by the application of compensation bias to a series of gates. In the light of these factors, architectural implications are then considered.

DOI
10.1088/0957-4484/17/18/008

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We theoretically investigate cross-talk in hyperfine gate control of donor-qubit quantum computer architectures, in particular the Kane proposal. By solving the Poisson and Schrödinger equations numerically for the gated donor system, we calculate the change in hyperfine coupling and thus the error in spin-rotation for the donor nuclear-electron spin system, as the gate-donor distance is varied. We thus determine the effect of cross-talk-the inadvertent effect on non-target neighbouring qubits-which occurs due to closeness of the control gates (20-30 nm). The use of compensation protocols is investigated, whereby the extent of cross-talk is limited by the application of compensation bias to a series of gates. In the light of these factors, architectural implications are then considered.
In the Kane silicon-based electron-mediated nuclear spin quantum computer architecture, phosphorous is doped at precise positions in a silicon lattice, and the P donor nuclear spins act as qubits. Logical operations on the nuclear spins are performed using externally applied magnetic and electric fields. There are two important interactions: the hyperfine and exchange interactions, crucial for logical qubit operations. Single qubit operations are performed by applying radio frequency magnetic fields resonant with targeted nuclear spin transition frequencies, tuned by the gate-controlled hyperfine interaction. Two qubit operations are mediated through the exchange interaction between adjacent donor electrons. It is important to examine how these two interactions vary as functions of experimental parameters. Here we provide such an investigation. First, we examine the effects of varying several experimental parameters: gate voltage, inter donor separation, donor depth below the silicon oxide interface and back gate depth, to explore how these variables affect the donor electro density. Second, we calculate the hyperfine interaction and the exchange coupling as a function of these parameters. These calculations were performed using an anisotropic effective mass Hamiltonian. The electric field potential was obtained using Technology Computer Aided Design software, and the interfaces were modelled as a barrier using a step function. We aim to provide relevant information for the experimental design of these devices and highlight the significance of environmental factors other than gate potential that affect the donor electron.
We propose a scheme for quantum information processing based on donor electron spins in semiconductors, with an architecture complementary to the original Kane proposal. We show that a na\"{\i}ve implementation of electron spin qubits provides only modest improvement over the Kane scheme, however through the introduction of global gate control we are able to take full advantage of the fast electron evolution timescales. We estimate that the latent clock speed is 100--1000 times that of the nuclear spin quantum computer with the ratio T2∕Tops{T}_{2}∕{T}_{\mathrm{ops}}T2​∕Tops​ approaching the 106{10}^{6}106 level.
The nuclear spin quantum computer proposed by Kane1 exploits as a qubit array 31P dopants embedded within a silicon matrix. Single-qubit operations are controlled by the application of electrostatic potentials via a set of metallic A gates, situated above the donors, on the silicon surface, that tune the resonance frequency of individual nuclear spins, and a globally applied RF magnetic field that flips spins at resonance. Coupling between qubits is controlled by the application of potentials via a set of J gates, between the donors, that induce an electron-mediated coupling between nuclear spins. We report the results of a study of the electric field and potential profiles arising within the Kane device from typical gate operations. The extent to which a single nuclear spin can be tuned independently of its neighbours, by operation of an associated A-gate, is examined and key design parameters in the Kane architecture are addressed. Implications for current fabrication strategies involving the implantation of 31P atoms are discussed. Solution of the Poisson equation has been carried out by simulation using a TCAD modeling package (Integrated Systems Engineering AG).
We demonstrate how gradient ascent pulse engineering optimal control methods can be implemented on donor-electron-spin qubits in Si semiconductors with an architecture complementary to the original Kane's proposal. We focus on the high-fidelity-controlled-NOT (CNOT) gate and explicitly find its digitized control sequences by optimizing its fidelity over the external controls of the hyperfine AAA and exchange JJJ interactions. This high-fidelity-CNOT gate has an error of about ${10}^{\ensuremath{-}6}$, below the error threshold required for fault-tolerant quantum computation, and its operation time of 100 ns is about three times faster than 297 ns of the proposed global control scheme. It also relaxes significantly the stringent distance constraint of two neighboring donor atoms of 10--20 nm as reported in the original Kane's proposal to about 30 nm in which surface AAA and JJJ gates may be built with current fabrication technology. The effects of the control voltage fluctuations, the dipole-dipole interaction, and the electron-spin decoherence on the CNOT gate fidelity are also discussed.