UNIVERSITY OF CALGARY Nonadiabatic Control for Quantum Information Processing and Biological Electron Transfer by Nathan S. Babcock A DISSERTATION SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS AND ASTRONOMY CALGARY, ALBERTA April, 2015 c Nathan S. Babcock 2015 Abstract In this Thesis, I investigate two disparate topics in the fields of quantum information processing and macromolecular biochemistry, inter-related by the underlying physics of nonadiabatic electronic transitions (i.e., the breakdown of the Born-Oppenheimer ap- proximation). The main body of the Thesis is divided into two Parts. In Part I, I describe my proposal for a two-qubit quantum logic gate to be implemented based on qubits stored using the total orbital angular momentum states of ultracold neutral atoms. I carry out numerical analyses to evaluate gate fidelity over a range of gate speeds, and I derive a simple criterion to ensure adiabatic gate operation. I propose a scheme to significantly improve the gate's fidelity without decreasing its speed. I contribute to the development of a \loophole-free" Bell inequality test based on the use of this gate by carrying out an order-of-magnitude feasibility analysis to assess whether the test is viable given realistic technological limitations. In Part II, I investigate electron transfer reaction experiments performed on native and mutant forms of the MADH{amicyanin redox complex derived from P. denitrificans. I implement molecular dynamics simulations of native and mutant forms of the solvated MADH{amicyanin complex. I analyze the resulting nuclear coordinate trajectories, both geometrically and in terms of electronic redox coupling. I find that the interprotein sol- vent dynamics of the mutant systems differ dramatically from those of the native system, and that the stability of an electron-transfer-mediating \water bridge" is compromised in the mutant complexes. I conclude that the mutations disrupt a protective \molecular breakwater" on the surface of amicyanin that stabilizes the interprotein water bridge. I discuss parallels between the nonadiabatic effects as they manifest themselves in the two systems, and I suggest how my findings in Part I promote technological developments to better characterize systems like that examined in Part II. ii Preface No storyteller has been able to dream up anything as fantastically unlikely as what really does happen in this mad Universe. |Robert A. Heinlein, 1973 [1] A decade ago, while completing my Science Baccalaureate (Honours Physics) at the University of Waterloo, I became interested in the prospect of molecular-scale engines and the question of what fundamental physical principles would enable their operation. In an effort to broach these questions, I wrote my undergraduate thesis, \Towards a Quantum Carnot Engine," under the supervision of Lucien Hardy at the Perimeter Institute. Dur- ing that investigation, I analyzed the work performed by a quantum mechanical particle confined to a classical infinite square potential and subjected to a thermodynamic cycle of quantum adiabatic and isothermal expansions and compressions. My investigation inspired more questions than it answered. What physical trait could distinguish the \engine" from the quantum \working fluid” it contained, if the engine too must be composed of quantum mechanical particles? In what limit could the engine cycle be described by a time-dependent classical potential? Finally, how could a ther- modynamic cycle be generated in the absence of explicit time-depedent control of the Hamiltonian describing all of the particles comprising engine and fluid? Confounded, I turned my attention to molecular biology to see what Nature had already discovered. This Thesis represents the outcome of my search so far. Nathan S. Babcock Calgary, Alberta 15 March 2015 iii Acknowledgement I am immensely grateful to my Supervisor Barry Sanders and to my Co-Supervisor Dennis Salahub for their astounding patience, enthusiasm, insight, and support. I am deeply indebted to them for their wisdom and subtle guidance in all matters related to my development as a scientist and as a person. I am grateful to the members of my Supervisory Committee, Robert Thompson and Sergei Noskov, for their thoughtful feedback and advice, and to the members of my Defence Committee, Peter Kusalik and Al´anAspuru-Guzik, for their experience and vision. I wish to express gratitude for the expertise of my scientific collaborators, Aur´elien de la Lande, Bernard L´evy, Mark Raizen, Jan Rez´aˇc,Ren´eStock,ˇ and Nathan Wiebe, and also for past guidance from Lucien Hardy, Stefan Idziak, and Ray Laflamme. For insightful discussions and words of encouragement, I wish to thank Ali Asadian, Ilya Balabin, Dave Bell, David Beratan, Mari Boesen, Hans Briegel, Cool Paul Carr, JJ Choquette, Victor Davidson, Paul Davies, Ivan Deutsch, David Feder, Graham Flem- ing, Gilad Gour, David Hayes, John Honek, Jonny Johannes, Stu Kauffman, Wolfgang Ketterle, Leah Kilvert, Judith Klinman, Ben Lavoie, Tony Leggett, Tina Chen Liu, Re- becca Lumsden, Rudy Marcus, Elliot Martin, Gerard Milburn, Rachid Ouyed, Ian Reid, Kevin Resch, Andrew Ringsmith, Marlan Scully, Michael Skotiniotis, Spiros Skourtis, Luca Turin, Vlatko Vedral, Gregor Weihs, and Ehsan Zahedinejad. I thank Robert Gen- nis for access to unpublished materials regarding biochemical experimental techniques. Computing facilities were provided by Westgrid and Compute Canada Calcul Canada. This work would not have been possible without financial support from both of my primary funding agencies, the Natural Sciences and Engineering Research Council of Canada and Alberta Innovates|Technology Futures. This financial trust has afforded me enormous academic and creative freedom to explore topics related to the physics of nanotechnology at my own discretion. iv To My Parents \As above, so below." v Table of Contents Abstract . ii Preface . iii Acknowledgement . iv Dedication . .v Table of Contents . vi List of My Written Contributions . ix List of Tables . xi List of Figures . xii List of Abbreviations . xiv 1 Summary of Contribution 1.1 Summary of Part I . .2 1.1.1 Motivation . .3 1.1.2 Object of Investigation . .4 1.1.3 Originality of My Contributions . .5 1.1.4 Scientific Impact . .6 1.1.5 Obstacles and Limitations . .7 1.2 Summary of Part II . .8 1.2.1 Motivation . .9 1.2.2 Object of Investigation . 11 1.2.3 Originality of My Contribution . 12 1.2.4 Scientific Impact . 14 1.2.5 Obstacles and Limitations . 15 1.3 Perspective . 16 2 Nonadiabatic Transitions 2.1 The Adiabatic Theorem . 18 2.1.1 Adiabatic Errors . 19 2.2 Adiabatic Description of Atoms and Molecules . 20 2.2.1 The Born-Oppenheimer Approximation . 21 2.3 Born-Oppenheimer Breakdown . 23 2.3.1 Validity of Assumption 1 (Nuclear Classicality) . 24 2.3.2 Validity of Assumption 2 (Adiabaticity) . 24 2.3.3 Statistical Mechanical Considerations . 25 2.4 Controlled Nonadiabatic Dynamics . 26 vi Part I 3 Quantum Information Processing 3.1 Quantum Information Theory . 30 3.2 Quantum Computing Architectures . 31 3.2.1 Circuit Model Quantum Computing . 32 3.2.2 One-Way Quantum Computing . 34 3.2.3 Adiabatic Quantum Computing . 35 3.3 Atomistic Implementations of Quantum Memory . 36 3.4 Exchanged-Based Entanglement of Neutral Atoms . 38 4 Entangling Identical Bosons via Exchange 4.1 Introduction: Coherent Control of Neutral Atoms . 42 4.2 Two-Particle Tweezer Hamiltonian . 45 4.3 Adiabatic Eigenstates . 46 4.4 Gate Operation . 50 4.5 Excitations to Non-Logical States . 51 4.6 Derivation of Adiabaticity Criterion . 55 4.7 Time-Dependent Simulations of Gate Operation . 57 4.8 Concluding Remarks . 59 5 Atomistic Bell Test Without Loopholes 5.1 Introduction: Completeness of Quantum Mechanics . 61 5.2 Design of Test Scheme . 64 5.2.1 Atomic Qubit Preparation . 65 5.2.2 Qubit Encoding . 65 5.2.3 Single Qubit Operations . 66 5.2.4 Entangling Operation . 66 5.2.5 Qubit Transport . 67 5.2.6 Rapid Measurement . 68 5.3 Spacelike-Separated Qubits . 68 5.4 Rapid Bell Measurements . 69 5.5 Concluding Remarks . 71 6 Improved Error-Scaling for Two-Qubit Entanglement 6.1 Introduction: Enhanced Adiabatic Evolutions . 73 6.2 Efficient Simulation of Approximately Adiabatic Evolutions . 75 6.3 Boundary Cancellation Technique . 77 6.4 Fidelity-Enhanced Adiabatic Exchange Gate . 79 6.5 Suppresion of Multiple Transitions . 80 6.6 Concluding Remarks . 81 vii Part II 7 Biological Electron Transfer 7.1 The Electron Transfer Integral . 87 7.1.1 McConnell's Model . 88 7.1.2 Hopfield’s Model . 89 7.1.3 The Pathway Model . 90 7.1.4 The Packing Density Model . 91 7.1.5 Ab Initio Models . 92 7.2 The Marcus Equation . 93 7.3 Complexity of Electron Transfer Kinetics . 95 7.3.1 True Electron Transfer Reactions . 96 7.3.2 Kinetically Gated Electron Transfer Reactions . 97 7.3.3 Kinetically Coupled Electron Transfer Reactions . 98 7.3.4 Dynamic Docking . 99 7.3.5 Non-Condon Effects . 100 7.4 Enzymatic Electron Transfer . 101 7.4.1 Copper Enzymes . 101 7.4.2 Cupredoxin Structure . 102 7.4.3 Methylamine Metabolism in Paracocous denitrificans ....... 103 7.4.4 True Electron Transfer from MADH to Native Amicyanin . 106 7.4.5 Species-Specific Electron Transfer . 107 7.4.6 Proline 52 Mutation of Amicyanin . 108 7.4.7 Methionine 51 Mutations of Amicyanin . 111 7.5 Further Considerations . 116 8 Water Bridges to Enhance Electron Transfer 8.1 Introduction: Water-Bridged Electron Transfer . 120 8.1.1 Simulation of Native MADH{Amicyanin Complex . 121 8.2 Production of Mutant Amicyanin Structures . 124 8.3 Simulations of the Mutant Complexes . 125 8.4 Comparison of Pathway and Packing Density Models . 125 8.5 Analysis of Solvent Organization . 127 8.6 Analysis of Electronic Transition Amplitudes . 130 8.7 Molecular Breakwater Hypothesis .