We examine exchange coupling in the Kate quantum computer, which consists of isolated spin-1/2 31P donors in a pure Si lattice. A calculation is made using full configuration interaction, a reasonably large basis set, and a simple physical model. Basis set convergence was not obtained, and increasing the size of the matrix further appears to be computationally impractical. We therefore consider a Gaussian basis set approach. A brief description of the McMurchie-Davidson algorithm for the expansion of SGTF functions into Hermite polynomials is given. We also give the results of
a single-donor computation in this basis.
We propose a scheme for electron spin quantum computing based on
electron spin in semiconductors. This scheme shares many similarities
with the existing Kane nuclear spin proposal. We show how quantum
computation may be carried out in this proposal, including single
qubit rotations and CNOT gate. We show how this control can
potentially lead to gate speeds 100-1000 times faster than the
existing nuclear spin proposal, and up to 106 times faster than a typical electron spin dephasing time, T2(e).
Quantum-dot Cellular Automata (QDCA) provide an interesting experimental system with which to study the interaction of a charge-based two-level system with the surrounding solid-state environment. This is particularly important given the recent interest in solid-state quantum computers using charge-qubits. We show that many of the properties of these qubits, coupling strength, tunnelling time, relaxation rate and dephasing time can be estimated using a QDCA cell like structure. Calculations are performed for the case of buried donors in silicon but the results are equally applicable to other forms of charge-qubit.
The feasibility of a charge based solid state quantum computing
depends to a great extent on the ability to overcome the presence
of noise sources such as Johnson noise in the gates and charge
traps due to defects in the material. In this paper, we study the
effects of dephasing from charge traps for the Si:P charge qubit.
The long coherence times of both nuclear and electron phosphorus donor spins in silicon make them promising qubits for a scalable quantum computer. In such a system, the single qubit operations could me implemented via the application of resonant RF fields, while the inter-qubit interactions are mediated via the exchange interaction between neighboring donor electrons. This interaction could be controlled, to some extent, via the application of potential biases to control electrodes, which would perturb the electron wavefunctions. The degeneracy of the conduction band minima in silicon leads to interference effects between the donor wavefunctions resulting in a strong dependence of the strength of the exchange coupling on the relative separation of the phosphorus donors, this can have significant consquences to the fabrication of a donor spin based quantum computer. We present calculations of the donor electron exchange coupling as a function of the relative donor position, using donor wavefunctions that have been calculated by direct diagonalisation of the system Hamiltonian, in a basis of the silicon conduction band Bloch functions, beyond the standard effective mass approximation. We consider the effects of non-Coulombic donor potentials, as well as an applied lattice strain, which breaks the degeneracy of the conduction band minima and can be used to damp the oscillatory behavior of the exchange energy. We discuss these results and their implications with respect to fabrication of a scalable donor spin quantum computer.
Direct single-spin detection for read-out in solid-state quantum computing architectures is a difficult problem due to the isolation of the spin qubit from its environment. Converting the problem to one of charge measurement is advantageous as we can measure the charge qubit using a single electron transistor (SET). The read-out state for the standard Si:P architecture -- a doubly occupied donor state D- -- results from spin-dependent electron tunneling between donors. Complications arise due to the low binding energy of this state, meaning existing adiabatic transfer schemes may cause ionisation of the D- state before measurement can be performed by the SET. We describe a new method for the read-out of spin qubits, using gated electric fields at resonance with the transition being measured, to resonantly transfer a single electron to the SET using small DC fields. In addition to this we propose an extension to this method where a far-infrared laser (FIR) induces the resonant transfer.
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).