Quantum Computation: Theory and Implementation by Edward Stuart Boyden III Submitted to the Department of Physics in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Physics and to the Department of Electrical Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degrees of Bachelor of Science in Electrical Engineering and Computer Science and Master of Engineering in Electrical Engineering and Computer Science at the Massachusetts Institute of Technology May 7, 1999 © 1999 MIT. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute paper and electronic copies of this thesis, and to grant others the right to do so. Author __________________________________________________________________ Edward S. Boyden III Physics and Media Group, MIT Media Laboratory Department of Physics Department of Electrical Engineering and Computer Science Certified by __________________________________________________________________ Neil Gershenfeld Professor of Media Technology, MIT Media Laboratory Thesis Supervisor Accepted by __________________________________________________________________ Arthur C. Smith Chairman, Department Committee on Graduate Theses Accepted by __________________________________________________________________ Prof. David E. Pritchard Senior Thesis Coordinator, Department of Physics Table of Contents 0.1 ABSTRACT ...........................................................................................................................................................5 0.2 ACKNOWLEDGEMENTS ..................................................................................................................................6 I. INTRODUCTION....................................................................................................................................................7 I.1. BACKGROUND ......................................................................................................................................................8 I.1.i. Quantum mechanics......................................................................................................................................8 I.1.ii. Information theory .....................................................................................................................................15 I.1.iii. Computability............................................................................................................................................18 I.1.iii.a. Automata Theory.................................................................................................................................................. 19 I.1.iii.b. Turing Machines .................................................................................................................................................. 22 I.1.iv. Complexity.................................................................................................................................................25 I.1.v. Algorithmic Complexity Theory..................................................................................................................30 I.1.vi Dynamics and computation........................................................................................................................30 I.2. ON QUANTUM COMPUTATION............................................................................................................................32 I.2.i. Fundamentals..............................................................................................................................................32 I.2.ii. Quantum Mechanics and Information .......................................................................................................34 I.2.iii. Quantum Logic .........................................................................................................................................42 II. MODELS OF QUANTUM COMPUTATION ..................................................................................................44 II.1. PRELIMINARY MODELS......................................................................................................................................44 II.2. QUANTUM GATE ARRAYS.................................................................................................................................45 II.3. INTERPRETING THE QUANTUM COMPUTER ........................................................................................................53 II.3.i. Proposals for quantum computers.............................................................................................................53 II.3.ii. Beyond the coprocessor paradigm ...........................................................................................................54 II.4 QUANTUM CELLULAR AUTOMATA ....................................................................................................................55 II.5. QUANTUM CHAOS AND DYNAMICS ....................................................................................................................57 III. POWER OF QUANTUM COMPUTATION...................................................................................................59 III.1. PROBLEMS AT WHICH QUANTUM COMPUTING IS GOOD...................................................................................59 III.1.i. Simulating Quantum Systems ...................................................................................................................59 III.1.ii. Factoring.................................................................................................................................................60 III.1.iii. Searching................................................................................................................................................61 III.1.iv. Other Problems.......................................................................................................................................64 III.2. FAULT-TOLERANT COMPUTATION....................................................................................................................65 IV. NUCLEAR MAGNETIC RESONANCE .........................................................................................................67 IV.1. NMR THEORY.................................................................................................................................................67 IV.1.i. Noninteracting spins.................................................................................................................................67 IV.1.ii. Interacting spins ......................................................................................................................................72 IV.1.iii. Spin phenomenology...............................................................................................................................74 IV.2. BULK SPIN RESONANCE QUANTUM COMPUTATION.........................................................................................76 IV.3. COHERENCE, SIGNALS, AND NMR COMPUTING ..............................................................................................79 V. THE ART OF QUANTUM COMPUTER PROGRAMMING: SYSTEM DESIGN .....................................83 V.1. A QUANTUM COMPUTER LANGUAGE ...............................................................................................................83 V.1.i. High-level language: a case study.............................................................................................................83 V.1.ii. System architecture and low-level control: QOS......................................................................................84 V.1.iii. Control structures for QOS: an implementation, ROS ............................................................................86 V.2. COMPILING FOR THE NMR QUANTUM COMPUTER ...........................................................................................90 V.3. SIMULATING .....................................................................................................................................................91 VI. HARDWARE IMPLEMENTATION OF THE NMR QUANTUM COMPUTER.......................................94 2 VI.1. HARDWARE OVERVIEW, MARK I.....................................................................................................................94 VI.1.i. Spectrometer.............................................................................................................................................94 VI.1.ii. Shimming ...............................................................................................................................................102 VI.2. HARDWARE OVERVIEW, MARK II .................................................................................................................107 VI.2.i. Testbed for the FPGA: the nanoTag reader ...........................................................................................107 VI.2.ii. A reconfigurable software radio portable NMR spectrometer: nanoNMR ...........................................110 Vi.2.ii.a. High-speed digital and analog design .............................................................................................................. 110 VII. CONCLUSION................................................................................................................................................113