240 research outputs found
Voltage Control of Exchange Coupling in Phosphorus Doped Silicon
Motivated by applications to quantum computer architectures we study the
change in the exchange interaction between neighbouring phosphorus donor
electrons in silicon due to the application of voltage biases to surface
control electrodes. These voltage biases create electro-static fields within
the crystal substrate, perturbing the states of the donor electrons and thus
altering the strength of the exchange interaction between them. We find that
control gates of this kind can be used to either enhance, or reduce the
strength of the interaction, by an amount that depends both on the magnitude
and orientation of the donor separation.Comment: 5 Pages, 5 Figure
Cross-talk compensation of hyperfine control in donor qubit architectures
We theoretically investigate cross-talk in hyperfine gate control of
donor-qubit quantum computer architectures, in particular the Kane proposal. By
numerically solving the Poisson and Schr\"{o}dinger equations 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 (20-30nm). The use of compensation protocols is
investigated, whereby the extent of crosstalk is limited by the application of
compensation bias to a series of gates. In light of these factors the
architectural implications are then considered.Comment: 15 pages, 22 figures, submitted to Nanotechnolog
Robust CNOT gates from almost any interaction
There are many cases where the interaction between two qubits is not
precisely known, but single qubit operations are available. In this paper we
show how, regardless of an incomplete knowledge of the strength or form of the
interaction between two qubits, it is often possible to construct a CNOT gate
which has arbitrarily high fidelity. In particular, we show that oscillations
in the strength of the exchange interaction in solid state Si and Ge structures
are correctable.Comment: 5 pages, 2 figure
Optically induced spin to charge transduction in donor spin read-out
The proposed read-out configuration D+D- for the Kane Si:P
architecture[Nature 393, 133 (1998)] depends on spin-dependent electron
tunneling between donors, induced adiabatically by surface gates. However,
previous work has shown that since the doubly occupied donor state is so
shallow the dwell-time of the read-out state is less than the required time for
measurement using a single electron transistor (SET). We propose and analyse
single-spin read-out using optically induced spin to charge transduction, and
show that the top gate biases, required for qubit selection, are significantly
less than those demanded by the Kane scheme, thereby increasing the D+D-
lifetime. Implications for singlet-triplet discrimination for electron spin
qubits are also discussed.Comment: 8 pages, 10 figures; added reference, corrected typ
Donor Electron Wave Functions for Phosphorus in Silicon: Beyond Effective Mass Theory
We calculate the electronic wave-function for a phosphorus donor in silicon
by numerical diagonalisation of the donor Hamiltonian in the basis of the pure
crystal Bloch functions. The Hamiltonian is calculated at discrete points
localised around the conduction band minima in the reciprocal lattice space.
Such a technique goes beyond the approximations inherent in the effective-mass
theory, and can be modified to include the effects of altered donor impurity
potentials, externally applied electro-static potentials, as well as the
effects of lattice strain. Modification of the donor impurity potential allows
the experimentally known low-lying energy spectrum to be reproduced with good
agreement, as well as the calculation of the donor wavefunction, which can then
be used to calculate parameters important to quantum computing applications.Comment: 10 pages, 5 figure
Effects of J-gate potential and interfaces on donor exchange coupling in the Kane quantum computer architecture
We calculate the electron exchange coupling for a phosphorus donor pair in
silicon perturbed by a J-gate potential and the boundary effects of the silicon
host geometry. In addition to the electron-electron exchange interaction we
also calculate the contact hyperfine interaction between the donor nucleus and
electron as a function of the varying experimental conditions. Donor
separation, depth of the P nuclei below the silicon oxide layer and J-gate
voltage become decisive factors in determining the strength of both the
exchange coupling and the hyperfine interaction - both crucial components for
qubit operations in the Kane quantum computer. These calculations were
performed using an anisotropic effective-mass Hamiltonian approach. The
behaviour of the donor exchange coupling as a function of the device parameters
varied provides relevant information for the experimental design of these
devices.Comment: 15 pages, 15 figures. Accepted for Journal of Physics: Condensed
Matte
A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength
We demonstrate how using two-qubit composite rotations a high fidelity
controlled-NOT (CNOT) gate can be constructed, even when the strength of the
interaction between qubits is not accurately known. We focus on the exchange
interaction oscillation in silicon based solid-state architectures with a
Heisenberg Hamiltonian. This method easily applies to a general two-qubit
Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity
when a single application of the composite rotations is combined with a modest
level of Hamiltonian characterisation. Operating the robust CNOT gate in a
suitably characterised system means concatenation of the composite pulse is
unnecessary, hence reducing operation time, and ensuring the gate operates
below the threshold required for fault-tolerant quantum computation.Comment: 9 pages, 8 figure
A theoretical investigation into the microwave spectroscopy of a phosphorus-donor charge-qubit in silicon: Coherent control in the Si:P quantum computer architecture
We present a theoretical analysis of a microwave spectroscopy experiment on a
charge qubit defined by a P donor pair in silicon, for which we calculate
Hamiltonian parameters using the effective-mass theory of shallow donors. We
solve the master equation of the driven system in a dissipative environment to
predict experimental outcomes. We describe how to calculate physical parameters
of the system from such experimental results, including the dephasing time,
, and the ratio of the resonant Rabi frequency to the relaxation rate.
Finally we calculate probability distributions for experimentally relevant
system parameters for a particular fabrication regime
Electron Exchange Coupling for Single Donor Solid-State Qubits
Inter-valley interference between degenerate conduction band minima has been
shown to lead to oscillations in the exchange energy between neighbouring
phosphorus donor electron states in silicon \cite{Koiller02,Koiller02A}. These
same effects lead to an extreme sensitivity of the exchange energy on the
relative orientation of the donor atoms, an issue of crucial importance in the
construction silicon-based spin quantum computers. In this article we calculate
the donor electron exchange coupling as a function of donor position
incorporating the full Bloch structure of the Kohn-Luttinger electron
wavefunctions. It is found that due to the rapidly oscillating nature of the
terms they produce, the periodic part of the Bloch functions can be safely
ignored in the Heitler-London integrals as was done by Koiller et. al. [Phys.
Rev. Lett. 88,027903(2002),Phys. Rev. B. 66,115201(2002)], significantly
reducing the complexity of calculations.
We address issues of fabrication and calculate the expected exchange coupling
between neighbouring donors that have been implanted into the silicon substrate
using an 15keV ion beam in the so-called 'top down' fabrication scheme for a
Kane solid-state quantum computer. In addition we calculate the exchange
coupling as a function of the voltage bias on control gates used to manipulate
the electron wavefunctions and implement quantum logic operations in the Kane
proposal, and find that these gate biases can be used to both increase and
decrease the magnitude of the exchange coupling between neighbouring donor
electrons. The zero-bias results reconfirm those previously obtained by
Koiller.Comment: 10 Pages, 8 Figures. To appear in Physical Review
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