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Controllable Few State Quantum Systems for Information Processing Controllable few state quantum systems for information processing by Jared Heath Cole BAppSc(AppPhys) BEng(Comm) (Hons) RMIT Submitted in total fulfilment of the requirements for the degree of Doctor of Philosophy School of Physics The University of Melbourne Australia October, 2006 The University of Melbourne Australia ABSTRACT Controllable few state quantum systems for information processing by Jared Heath Cole Chairperson of Supervisory Committee: Prof. G. N. Taylor School of Physics This thesis investigates several different aspects of the physics of few state quan- tum systems and their use in information processing applications. The main focus is performing high precision computations or experiments using imperfect quantum systems. Specifically looking at methods to calibrate a quantum system once it has been manufactured or performing useful tasks, using a quantum system with only limited spatial or temporal coherence. A novel method for characterising an unknown two-state Hamiltonian is pre- sented which is based on the measurement of coherent oscillations. The method is subsequently extended to include the effects of decoherence and enable the estima- tion of uncertainties. Using the uncertainty estimates, the achievable precision for a given number of measurements is computed. This method is tested experimentally using the nitrogen-vacancy defect in diamond as an example of a two-state quantum system of interest for quantum information processing. The method of character- isation is extended to higher dimensional systems and this is illustrated using the Heisenberg interaction between spins as an example. The use of buried donors in silicon is investigated as an architecture for realising quantum-dot cellular automata as an example of quantum systems used for classical information processing. The interaction strengths and time scales are calculated and both coherent and incoherent evolution are assessed as possible switching mecha- nisms. The effects of decoherence on the operation of a single cell and the scaling behaviour of a line of cells is investigated. The use of type-II quantum computers for simulating classical systems is studied as an application of small scale quantum computing. An algorithm is developed for simulating the classical Ising model using Metropolis Monte-Carlo where random number generation is incorporated using quantum superposition. This suggests that several new algorithms could be developed for a type-II quantum computer based on probabilistic cellular automata. This is to certify that (i) the thesis comprises only my original work, (ii) due acknowledgement has been made in the text to all other material used, (iii) the thesis is less than 100,000 words in length, exclusive of table, maps, bibli- ographies, appendices and footnotes. I authorize the Head of the School of Physics to make or have made a copy of this thesis to any person judged to have an acceptable reason for access to the information, i.e., for research, study or instruction. Signature Date ACKNOWLEDGMENTS There are a number of people, without whom this thesis would never have seen the light of day. First of all, I must thank both my official and unofficial supervisors. Steven Prawer for getting me excited about quantum computing in the first place, and for many useful discussions. Lloyd Hollenberg for his untiring support and as- sistance, both technical and professional, and for teaching me how to be a theorist. Cameron Wellard and Andrew Greentree for answering my many questions (espe- cially the stupid ones) and for always being available to argue over technicalities. I also thank Salvy Russo who first introduced me to the world of theoretical physics and who has provided many a coffee and a chat. During my candidature, I was able to visit several other institutions and received support and warm hospitality from all of them. Thanks must go to Frank Wilhelm and Jan von Delft at LMU M¨unchen and Jason Ralph at the University of Liver- pool. I’m especially indebted to Torsten G¨abel, Fedor Jelezko and J¨org Wrachtrup at the University of Stuttgart for the beautiful experimental data which constitutes chapter 6. I must also thank Sonia Schirmer and Daniel Oi at the University of Cam- bridge for encouragement and technical support for all of the work on Hamiltonian characterisation, both in Melbourne and during my visit to Cambridge. Closer to home, special thanks go to Simon Devitt for useful discussions, both technical and nontechnical, in many locations all over the world. Also, the inhab- itants of room 607, Vince, Damien and Joo Chew and the other members of the DMP group and the 6th floor. They made the School of Physics a fantastic place to work, where I always felt welcome, challenged and stimulated. It was also these people, ably assisted by the School of Physics pool table, who kept me sane ....... or at least limited the damage. Finally I’d like to thank my family, without them I would not have the drive v or confidence to get through so many years of university. Sharna for the use of her hideaway for the dark days during writeup and Tahlia for proof reading all 200+ pages. My parents, without whom I would not be here (figuratively and literally), Dad for encouraging my never ending questions about the world and Mum for never ending support. Last but certainly not least, I must thank Danielle for everything, for being both a source of strength and inspiration and for always being there. LIST OF PUBLICATIONS During the course of this project, a number of public presentations have been made, which are based on the work presented in this thesis. They are listed here for reference. REFEREED PUBLICATIONS J. H. Cole, L. C. L. Hollenberg and S. Prawer. An algorithm for simulating • the Ising model on a type-II quantum computer. Computer Physics Commu- nication, vol. 161, no. 1-2, pg. 18-26, 2004. A. D. Greentree, J. H. Cole, A. R. Hamilton and L. C. L. Hollenberg. Coherent • electronic transfer in quantum dot systems using adiabatic passage. Physical Review B, vol. 70, no. 235317, 2004. J. H. Cole, A. D. Greentree, C. J. Wellard, L. C. L. Hollenberg and S. Prawer. • Quantum-dot cellular automata using buried dopants. Physical Review B, vol. 71, no. 115302, 2005. J. H. Cole, S. G. Schirmer, A. D. Greentree, C. J. Wellard, D. K. L. Oi and • L. C. L. Hollenberg. Identifying an experimental two-state Hamiltonian to arbitrary accuracy. Physical Review A, vol. 71, no. 062312, 2005. J. H. Cole, A. D. Greentree, D. K. L. Oi, S. G. Schirmer. C. J. Wellard and • L. C. L. Hollenberg. Identifying a two-state Hamiltonian in the presence of decoherence. Physical Review A, vol. 73, no. 062333, 2006. S. J. Devitt, J. H. Cole and L. C. L. Hollenberg. Scheme for direct measurement • of a general two-qubit Hamiltonian. Physical Review A, vol. 73, no. 052317, 2006. J. H. Cole, S. J. Devitt and L. C. L. Hollenberg. Precision characterisation • of two-qubit Hamiltonians via entanglement mapping. Journal of Physics A, vol. 39, no. 47, pg. 14649-14658, 2006. A. D. Greentree, C. Tahan, J. H. Cole and L. C. L. Hollenberg. Quantum • phase transitions of light. Nature Physics, vol. 2, no. 12, pg. 856-861, 2006. vii REFEREED CONFERENCE PROCEEDINGS S. G. Schirmer, A. Kolli, D. K. L. Oi and J. H. Cole. Experimental Hamiltonian • identification for qubits subject to multiple independent control mechanisms. Quantum Communication, Measurement and Computing, vol. 734, pg. 79-82, 2004. J. H. Cole, A. D. Greentree, C. J. Wellard, L. C. L. Hollenberg and S. Prawer. • Measuring decoherence properties of charge qubits using buried donor cellular automata. SPIE Conference Proceedings, vol. 5650, pg. 96, 2005. A. D. Greentree, J. H. Cole, A. R. Hamilton and L. C. L. Hollenberg. Scaling of • coherent tunneling adiabatic passage in solid-state coherent quantum systems. SPIE Conference Proceedings, vol. 5650, pg. 15, 2005. L. C. L. Hollenberg, A. D. Greentree, C. J. Wellard, A. G. Fowler, S. J. Devitt • and J. H. Cole. Qubit transport and fault-tolerant architectures. Proceed- ings of the 2006 International conference on nanoscience and nanotechnology, Brisbane, Australia , 2006. CONFERENCE ABSTRACTS J. H. Cole, A. D. Greentree, C. J. Wellard and L. C. L. Hollenberg. Quantum- • dot cellular automata using buried dopants. 5th Quantum Information Pro- cessing and Communication Workshop, Rome, Italy, 2004. J. H. Cole, A. D. Greentree, C. J. Wellard and L. C. L. Hollenberg. Systematic • Hamiltonian identification of two-level systems. Australian Institute of Physics - National Congress, Canberra, Australia, 2005. J. H. Cole, A. D. Greentree, C. J. Wellard, S. G. Schirmer, D. K. L. Oi and • L. C. L. Hollenberg. Systematic Hamiltonian identification of two-level systems with decoherence. CMI Summer School, Belfast, Northern Ireland, 2005. J. H. Cole, A. D. Greentree, C. J. Wellard, S. G. Schirmer, D. K. L. Oi • and L. C. L. Hollenberg. Systematic Hamiltonian identification of finite state systems. Sir Marcus Oliphant conference on the frontiers of quantum nano- science, Noosa, Australia, 2006. LIST OF ABBREVIATIONS The following acronyms are used throughout this thesis. BDCA Buried Donor Cellular Automata CA Cellular Automata CMOS Complementary Metal-Oxide-Semiconductor DFT Discrete Fourier Transform EM Electromagnetic FFT Fast Fourier Transform FWHM Full Width Half Maximum MC Monte Carlo MLE Maximum Likelihood Estimation MPP Minimum Phase Point NMR Nuclear Magnetic Resonance NV Nitrogen Vacancy ODMR Optically Detected Magnetic Resonance QCA Quantum Cellular Automata QDCA Quantum-Dot Cellular Automata QED Quantum ElectroDynamics QFT Quantum Fourier Transform QIP Quantum Information Processing QPT Quantum Process Tomography QST Quantum State Tomography SEP Someone Else’s Problem T2QC Type-II Quantum Computer ix CONTENTS 1 Introduction 1 1.1 Layout and publication of material in this thesis . ..... 3 2 Background 5 2.1 (Quantum)informationprocessing .
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