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Shi Uchicago 0330D 15559.Pdf THE UNIVERSITY OF CHICAGO COMPILATION, OPTIMIZATION AND VERIFICATION OF NEAR-TERM QUANTUM COMPUTING A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS BY YUNONG SHI CHICAGO, ILLINOIS DECEMBER 2020 Copyright c 2020 by Yunong Shi All Rights Reserved TABLE OF CONTENTS LIST OF FIGURES . vi LIST OF TABLES . x ACKNOWLEDGMENTS . xi ABSTRACT . xiii 1 THESIS OVERVIEW . 1 1.1 Breaking Abstractions in the Quantum Computing Stack . .1 1.2 Reliable Quantum Software by Formal Verification . .3 2 INTRODUCTION TO QUANTUM COMPUTING . 5 2.1 Quantum Computing Basics . .5 2.2 Quantum Algorithms . .7 2.2.1 Shor’s algorithm . .7 2.2.2 Grover algorithm . .9 2.2.3 Quantum simulation . 11 2.2.4 Variational Quantum Eigensolver . 12 2.2.5 Quantum Approximation Optimization Algorithm . 13 2.3 Quantum Architectures . 14 2.3.1 The DiVincenzo criteria . 14 2.3.2 Superconducting QIP platform . 15 2.3.3 Trapped ion QIP platform . 16 2.4 Software Stack of Near-term Quantum Computing . 17 3 OPTIMIZED QUANTUM COMPILATION OF AGGREGATED INSTRUCTIONS . 19 3.1 Quantum Compilation . 19 3.1.1 Solovay Kitaev theorem . 20 3.1.2 Other compilation methods . 23 3.2 Quantum Control . 25 3.2.1 Basic Lie algebra . 26 3.2.2 Controllability . 27 3.2.3 The KAK decomposition . 28 3.2.4 Quantum optimal control using numerical methods . 29 3.3 Breaking the Abstraction of ISA using Aggregated Instructions . 31 3.4 Compilation Methodology . 32 3.4.1 An example of QAOA circuit . 32 3.4.2 Methodology overview . 36 3.4.3 Compilation frontend . 37 3.4.4 Compiler backend . 40 3.4.5 Optimal control unit . 41 3.4.6 Verification . 41 iii 3.5 Instruction Aggregation . 42 3.5.1 Action space for instruction aggregation . 42 3.5.2 Diagonal unitaries aggregation for commutativity detection . 43 3.5.3 Instruction aggregation . 44 3.6 Evaluation . 44 3.6.1 Experimental setup . 45 3.6.2 Benchmark methodology . 46 3.6.3 Latency . 46 3.7 Discussion . 47 3.7.1 Commutativity vs scheduling . 47 3.7.2 Parallelism vs instruction width . 47 3.7.3 Spatial locality vs aggregation . 47 3.7.4 Information encoding scheme vs pulse optimization . 48 3.8 Related Work . 49 4 FAULT TOLERANT PREPARATION OF APPROXIMATE GKP STATES . 51 4.1 Quantum Harmonic Oscillator . 52 4.2 Gottesman Kitaev Preskill State . 57 4.2.1 Perfect GKP states . 57 4.2.2 Approximated GKP states . 58 4.3 Prepare a GKP state — the Phase Estimation Protocol . 62 4.3.1 The PE measurement operator of 1 round . 62 4.3.2 The PE measurement operator of M rounds . 63 4.3.3 What is a good state? . 64 4.3.4 The probability of measuring 0 or 1 at each round . 67 4.3.5 PE strategies . 71 4.4 Goodness of Approximate GKP States . 72 4.5 Fault-tolerant Definitions . 75 4.6 Fault-tolerant Phase Estimation Protocol . 78 4.6.1 Brief review of the phase estimation protocol for preparing approximate GKP states . 79 4.6.2 (1; δ~) fault-tolerant state preparation using phase estimation . 80 4.6.3 Goodness of approximate j0~i states obtained from the noise free phase estimation protocol . 87 4.7 Circuit QED Implementation . 87 4.7.1 State evolution in the dispersive regime . 87 4.7.2 Full noise analysis and master equation results. 91 5 THE CERTIQ VERIFICATION FRAMEWORK . 98 5.1 The Need and Challenges of Formal Verification in Quantum Compilation . 98 5.2 CertiQ Verification Framework . 99 5.2.1 CertiQ design . 99 5.2.2 The Qiskit compiler . 101 5.3 The CertiQ Workflow . 104 5.4 The Verified CertiQ Library . 106 iv 5.5 Quantum Circuit Calculus . 109 5.6 The CertiQ Synthesizer . 113 5.6.1 Generating verification conditions . 113 5.6.2 Generating execution code . 115 5.7 The CertiQ Verifier . 116 5.8 Case Studies . 117 5.8.1 The optimize 1q gate pass . 117 5.8.2 commutation passes . 119 5.8.3 routing passes . 120 5.9 Evaluation . 121 5.10 Related Work . 122 6 CONCLUSION . 124 6.1 Thesis Review . 124 6.2 Future Directions for Near-term Quantum Architecture Design . 126 6.2.1 Pulse-level compilation . 126 6.2.2 Noise-Tailoring Compilation . 127 6.2.3 Algorithm-Level Error Correction . 127 6.2.4 Dissipation-Assisted Error Mitigation . 128 6.3 Future Directions for Verification of Quantum Computation . 128 6.3.1 Verified Quantum Toolchain . 128 6.3.2 Verified Fault Tolerant Quantum Computing . 129 APPENDICES . 130 A PHYSICAL QUANTUM GATES . 131 B NUMERIC SIMULATION DETAILS IN THE PHASE ESTIMATION PROTOCOL . 132 B.1 Shift error arising from amplitude damping before the controlled-displacement gate 132 B.2 Analytic derivation of the unitary operator describing the evolutionp of the qubit- cavity system during the implementation of thep controlled-D( 2π) gate. 133 B.2.1 Implementation of the controlled-D( 2π) gate in the lab frame. 133 B.2.2 Including the Kerr non-linearity . 145 B.2.3 Controlled-displacement gate in the rotating frame . 145 B.2.4 Effects of the non-linear dispersive shift and Kerr term on the unitary evo- lution of the qubit-cavity system . 147 B.2.5 Details of numerical simulation . 149 C DETAILS OF THE CERTIQ FRAMEWORK . 151 C.1 Syntax of Quantum Circuits supported in CertiQ . 151 C.2 Shortcut Lemmas . 151 C.3 The CertiQ Interface . ..
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