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Program Manager
A/Prof Lloyd C.L. Hollenberg - University of Melbourne

Device Modelling Researchers
Dr Cameron Wellard - University of Melbourne
Dr Chris Pakes - University of Melbourne
Dr John McIntosh - University of Melbourne

Device Modelling Students
Mr Austin Fowler
Mr Francesco Parisoli
Mr Vincent Conrad
Mr Matthew Testolin
Mr Joo Chew Ang
Mr Tim Starling
Mr Jared Cole
Mr James Hoadley
Mr Simon Devitt

Collaborating Centre Researchers
A/Prof David Jamieson - University of Melbourne
Prof Robert Clark - University of New South Wales
A/Prof Andrew Dzurak - University of New South Wales
A/Prof Alex Hamilton - University of New South Wales
Dr David Reilly - University of New South Wales
Dr Fred Green - University of New South Wales
Prof Gerard Milburn - University of Queensland
Dr Hsi-Sheng Goan - University of Queensland
A/Prof Sean Smith - University of Queensland
Ms Louise Kettle - University of Queensland
Mr Charles Hill - University of Queensland

Other Collaborating Researchers
Mr Sean Barrett - University of Cambridge, UK
Prof H.C. Pauli - MPIK, Germany
Mr. W. Haig - Department of Defence, Australia
Dr S. Russo - RMIT University, Australia
Mr Nick Wilson - RMIT University, Australia

Program Description
The main objective of the program is to provide a realistic theoretical description of the Kane quantum computer architecture, which is important not only in the understanding of the operation of the device, but also as a guide to the fabrication process, and to develop new ideas for quantum computing in the solid state.

A realistic description of the two qubit device, including readout, requires detailed modelling and simulation of four coupled donor electron-nucleon systems in the silicon environment, together with a formidable array of time dependent gate potentials. The theoretical treatment of this complex quantum system is therefore approached in various stages. To this end, there are a number of areas currently being worked on across the three nodes, including; single qubit operation, two qubit interaction, readout processes, and the effect of decoherence.

Charge based buried dopant quantum computing
Through collaboration across several Centre programs, a detailed proposal for charge qubit quantum computing based on individually placed dopants in semiconductors was completed. The buried charge qubit (shown in the figure for the case Si:P) consists of two dopant atoms ~50nm apart in a semiconductor crystal, one of which is singly ionised. The lowest two energy states of the remaining electron form the logical states of the qubit.

Surface electrodes B and S control the qubit through applied voltage pulses and a single electron transistor (SET) operating near the quantum limit provides fast readout. Current calculations centre on the effect of charge traps on the decoherence time and operation of the charge qubit architectures.

Modelling gate potentials and qubit operation
TCAD simulation has been used extensively to provide potential profiles corresponding to applied gate voltages. Shown below in Figure 2 (left) is a typical situation considered - a series of gates placed above donor qubits buried 20nm below the oxide layer. The various geometrical parameters can be altered quite easily, and the resulting potential profiles used in the calculation of the donor electron wave function response (right).

Donor Electron Wave Function
We have made considerable progress in understanding the nature and response of the donor electron wave function (DEWF) to external gate potentials. This is an important problem which holds the key to understanding the physics of these quantum devices, whether spin or charge based. It has long been recognised that the DEWF for shallow P donors in silicon is well described by the so-called Kohn-Luttinger form where one takes equal contributions from each of the six conduction band minima. In the presence of surface gate structure and associated time dependent electrostatic potentials the situation is considerably more complex. One must re-solve for the DEWF in the presence of the varying external potentials, for each new device configuration. We have completed a computational framework in which the quantum mechanics of the donor electron can be solved for directly in k-space including TCAD potentials.

Device operation simulations and fidelity determination
Time domain simulations (bottom right) of the effective spin dynamics of the two-qubit Kane system were extended to include the effects of both nuclear and electron dephasing. The error rate of the adiabatic CNOT operation was determined for a range of electron and nuclear dephasing times, as shown below (top left). As one can see, the electron coherence time T2 has a strong effect on the overall error rate: for T2 of order 60 ms the CNOT gate error is less than 10-4, which is within the quantum error correction threshold.

A similar study was undertaken on the fidelity of readout preparation stage (bottom left). Again, the process is highly sensitive to the electron decoherence time, and for e of order 60 ms the error is quite low.

Simulations of Quantum Error Correction and quantum algorithms
With the determination of the level of gate errors expected for one and two qubit gates we are now in a position to study the effect of these errors on error correction (5 qubit encoded storage and 7 qubit encoded swap) and the implementation of quantum algorithms with imperfect gates.

The Quantum Fourier Transform (QFT) lies at the heart of many quantum algorithms, and relies on the ability to carry out precise single qubit rotations with an accuracy that increases exponentially with the number of qubits (or problem instance). An interesting question therefore is how errors in the QFT arising from single qubit rotation errors affect Shor's factoring algorithm, for instance. We have simulated the factoring algorithm with rotation errors /2k for problems involving up to 28 digits. As the results in the figure below show, Shor's algorithm is remarkably robust against such errors.



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