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The University of Chicago Quantum Computing with Distributed Modules a Dissertation Submitted to the Faculty of the Division Of

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The University of Chicago Quantum Computing with Distributed Modules a Dissertation Submitted to the Faculty of the Division Of THE UNIVERSITY OF CHICAGO QUANTUM COMPUTING WITH DISTRIBUTED MODULES 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 NELSON LEUNG CHICAGO, ILLINOIS MARCH 2019 Copyright c 2019 by Nelson Leung All Rights Reserved TABLE OF CONTENTS LIST OF FIGURES . vi LIST OF TABLES . viii ACKNOWLEDGMENTS . ix ABSTRACT . x PREFACE............................................ 1 1 QUANTUM COMPUTING . 2 1.1 Introduction to Quantum Computing . .2 1.2 High-Level Description of Some Quantum Algorithms . .3 1.2.1 Grover’s algorithm . .3 1.2.2 Shor’s algorithm . .3 1.2.3 Variational Quantum Eigensolver (VQE) . .4 1.3 Quantum Architectures . .4 1.3.1 Trapped Ions . .4 1.3.2 Silicon . .5 1.3.3 Superconducting qubits . .5 1.4 Thesis Overview . .6 2 CIRCUIT QUANTUM ELECTRODYNAMICS . 7 2.1 Quantization of Quantum Harmonic Oscillator . .7 2.2 Circuit Quantum Harmonic Oscillator . 10 2.3 Josephson Junction . 12 2.4 Quantization of Transmon Qubit . 13 2.5 Quantization of Split Junction Transmon Qubit with External Flux . 16 2.6 Coupling between Resonators . 18 2.7 Dispersive Shift between Transmon and Resonator . 21 3 CONTROLLING SUPERCONDUCTING QUBITS . 23 3.1 Charge Control . 23 3.2 Flux Control . 25 3.3 Transmon State Measurement . 25 3.4 Cryogenic Environment . 26 3.5 Microwave Control Electronics . 26 3.5.1 Oscillator . 26 3.5.2 Arbitrary waveform generator . 27 3.5.3 IQ mixer . 27 3.6 Other Electronics . 28 3.7 Microwave Components . 28 3.7.1 Attenuator . 28 iii 3.7.2 Filter . 29 3.7.3 Isolator . 29 3.7.4 Amplifier . 29 3.8 Software For Quantum Operations and Measurements . 30 3.8.1 Hardware Drivers . 30 3.8.2 Essential properties . 30 3.9 Putting all together: Cryogenic setup and control instrumentation . 32 4 QUANTUM OPTIMAL CONTROL . 34 4.1 Introduction . 34 4.2 Theory . 36 4.2.1 Important types of cost function contributions . 38 4.2.2 Gradient evaluation . 42 4.3 Implementation . 45 4.4 Performance Benchmarking . 48 4.5 Showcase Applications . 50 4.5.1 CNOT gate for two transmon qubits . 51 4.5.2 Reducing duration of state transfer . 53 4.5.3 Generating photonic Schrodinger¨ cat states . 54 4.5.4 Hadamard transform and GHZ state preparation . 56 4.6 Analytical gradients and algorithms . 58 4.6.1 Gradient for C1: target-gate infidelity . 60 4.6.2 Gradient for C2: target-state infidelity . 61 4.6.3 Gradient for C5: occupation of forbidden state . 62 4.6.4 Discussion of the algorithms . 64 4.7 Conclusion . 64 5 MULTIMODE CIRCUIT QED . 66 5.1 Introduction . 66 5.2 Multimode quantum memory . 68 5.3 Stimulated vacuum Rabi oscillations . 71 5.4 Universal quantum control . 73 5.5 Multimode entanglement . 77 5.6 Multimode quantum memory Hamiltonian . 78 5.7 Parametric control Hamiltonian . 79 5.8 Device design and fabrication . 83 5.9 Transmon and readout resonator properties . 84 5.10 Stimulated vacuum Rabi oscillations with multiple transmon levels . 87 5.11 Correcting for the transmission profile of the flux bias line . 88 5.12 Coupling between the transmon and the multimode memory . 90 5.13 Hamiltonian tomography . 92 5.14 Coherence of the multimode memory . 93 5.15 Single-mode gate calibration . 94 5.16 Randomized benchmarking . 96 5.17 Two mode gates using sideband transitions . 97 iv 5.18 Phase error corrections to two-mode gates . 98 5.19 CZ gate phase calibration sequences . 102 5.20 Two-mode quantum state tomography . 105 5.21 Process tomography of two-mode gates . 108 5.22 Preparation of entangled states . 112 5.23 GHZ entanglement witness . 114 5.24 Conclusion . 115 6 QUANTUM COMMUNICATIONS BETWEEN MULTIMODE MODULES . 117 6.1 Introduction . 117 6.2 Photonic communication by parametric interaction . 119 6.3 Multimode communication channel . 121 6.4 Bidirectional communication . 123 6.5 Bell state entanglement . 125 6.6 Device Hamiltonian . 127 6.7 Sideband interaction and calibrations . 132 6.8 Master equation simulation . 137 6.9 Single pass loss limitation of transfer fidelity . 141 6.10 Readout and state tomography . 143 6.11 Online Gaussian process for Bell state optimization . 145 6.12 Heralding protocol for state transfer . 146 6.13 Conclusion . 148 7 REFERENCES . 150 v LIST OF FIGURES 3.1 Detailed schematic of the experimental setup . 32 4.1 Computational network graph for quantum optimal control . 41 4.2 Sample computational graph for automatic differentiation . 43 4.3 Benchmarking comparison between GPU and CPU . 48 4.4 Control pulses and evolution of quantum state population for a CNOT gate acting on two transmon qubits . 50 4.5 Minimizing evolution time needed for a high-fidelity state transfer . 52 4.6 Cat state generation . 54 4.7 Performance of optimal control algorithm as a function of qubit number . 58 5.1 Random access superconducting quantum information processor . 67 5.2 Stimulated vacuum Rabi oscillations.
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