Micromachined Quantum Circuits A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Teresa Brecht Dissertation Director: Professor Robert J. Schoelkopf December 2017 c 2017 by Teresa Brecht. All rights reserved. ISBN 978-1-387-00572-7 i Abstract Micromachined Quantum Circuits Teresa Brecht 2017 Quantum computers will potentially outperform classical computers for certain applications by employing quantum states to store and process information. However, algorithms using quantum states are prone to errors through continuous decay, posing unique challenges to engineering a quantum system with enough quantum bits and sufficient controls to solve interesting problems. A promising platform for implementing quantum computers is that of circuit quantum electrody- namics (cQED) using superconducting qubits. Here, two energy levels of a resonant circuit en- dowed with a Josephson junction serve as the qubit, which is coupled to a microwave-frequency electromagnetic resonator. Modern quantum circuits are reaching size and complexity that puts extreme demands on input/output connections as well as selective isolation among internal ele- ments. Continued progress will require adapting sophisticated 3D integration and RF packaging techniques found in today’s high-density classical devices to the cQED platform. This novel tech- nology will take the form of multilayer microwave integrated quantum circuits (MMIQCs), com- bining the superb coherence of three-dimensional structures with the advantages of lithographic integrated circuit fabrication. Several design and fabrication techniques are essential to this new physical architecture, notably micromachining, superconducting wafer bonding, and out-of-plane qubit coupling. This thesis explores these techniques and culminates in the design, fabrication, and measurement of a two-cavity/one-qubit MMIQC featuring qubit coupling to a superconducting micromachined cavity resonator in silicon wafers. Current prototypes are extensible to larger scale MMIQCs for scalable quantum information processing. ii Contents Abstract ii Contents iii Acknowledgements vii List of Publicationsx List of Figures xii List of Tables xv List of Abbreviations xvi List of Physical Constants xviii List of Symbols xix 1 Introduction1 1.1 Thesis synopsis...................................2 2 Quantum computing5 2.1 Bits and qubits....................................5 2.2 Physical realizations................................8 2.3 Decoherence of qubits...............................9 2.4 Quantum computation............................... 11 2.4.1 The DiVincenzo criteria.......................... 12 2.5 Quantum error correction............................. 14 2.6 Modular architecture for quantum computing................. 17 3 Circuit quantum electrodynamics 19 3.1 Quantum electrodynamics............................. 20 3.2 Quantum electromagnetic oscillators....................... 21 3.3 Josephson junction qubits............................. 23 3.4 Circuit QED..................................... 30 3.4.1 Strong dispersive regime......................... 31 iii 3.4.2 Qubit readout................................ 33 3.4.3 Multimode generalization......................... 33 3.4.4 Black-box quantization analysis..................... 33 3.5 Experimental implementations.......................... 38 3.5.1 Engineered interaction........................... 38 3.5.2 3D Cavity cQED.............................. 44 3.6 A dynamic toolbox................................. 46 4 Multilayer microwave integrated quantum circuits 48 4.1 Scalability...................................... 48 4.1.1 Introduction................................. 48 4.1.2 Challenges in scaling cQED circuits................... 51 4.2 Quantum hardware of the future......................... 55 4.3 Characteristics of MMIQCs derived from existing technology...................................... 59 4.3.1 3D cavities and isolation.......................... 59 4.3.2 3D transmission lines........................... 60 4.3.3 Vertical interconnects............................ 61 4.3.4 Vias...................................... 63 4.3.5 Dense I/O connectorization........................ 65 4.4 Prior high-density multilayer superconducting ICs............... 66 4.4.1 RSFQ and RQL circuits........................... 66 4.4.2 Detectors................................... 68 4.5 MMIQC development............................... 68 4.5.1 Hybridization opportunities....................... 68 4.5.2 New challenges............................... 69 4.6 Conclusion...................................... 70 5 Microwave resonators 72 5.1 Physical realizations................................ 73 5.1.1 Planar transmission line resonators................... 73 5.1.2 Compact resonators............................ 74 5.1.3 3D cavity resonators............................ 74 5.1.4 Hybrid forms................................ 76 5.2 Loss mechanisms.................................. 78 5.2.1 External loss................................. 79 5.2.2 Radiation loss................................ 81 5.2.3 Conductor loss............................... 86 5.2.4 Dielectric loss................................ 88 5.2.5 Seam loss.................................. 90 5.3 Resonator measurement methodology...................... 92 5.3.1 Superconducting resonator measurement setup............ 92 5.3.2 Fitting resonance line-shapes to extract quality factor......... 93 5.3.3 Extracting photon number......................... 97 iv 5.4 Seam loss in 3D cavities.............................. 102 5.4.1 Microwave cavity choke.......................... 103 5.4.2 Aluminum 3D cavities with various seam configurations....... 105 5.4.3 Indium 3D cavities............................. 107 5.4.4 Indium gasket................................ 108 5.5 Conclusion...................................... 109 6 Micromachined cavity resonators 110 6.1 Introduction..................................... 110 6.2 Fabrication...................................... 110 6.2.1 Bulk etching................................. 110 6.2.2 Electroplating................................ 114 6.2.3 Bonding................................... 114 6.3 Coupling....................................... 115 6.3.1 Pin coupling................................. 115 6.3.2 Transmission line to aperture coupling................. 117 6.3.3 Lateral loop coupling........................... 118 6.3.4 Lateral CPW coupling........................... 123 6.4 Frequency shift in wet-etched rectangular cavity................ 125 6.5 Summary....................................... 129 7 Superconducting wafer bonding with indium 130 7.1 Background on wafer bonding.......................... 131 7.2 Indium bump bonding............................... 133 7.2.1 Fabrication.................................. 135 7.3 Mechanical considerations............................. 137 7.3.1 Deformation of bumps under bond and separation........... 139 7.3.2 Shear tests of indium bonds........................ 141 7.4 Bonded stripline resonators............................ 143 7.5 Indium 3D resonators................................ 147 7.5.1 Power dependence with TLS signature................. 148 7.5.2 Cases of nonlinear resonance....................... 150 7.6 Temperature dependence of 3D indium microwave resonator........ 155 7.7 DC resistivity of indium versus temperature.................. 159 7.8 Conclusion...................................... 161 8 Transmons in the MMIQC 163 8.1 Coupling challenge................................. 163 8.2 The aperture transmon............................... 164 8.2.1 Fields of the aperture transmon...................... 165 8.2.2 Aperture transmon and cavity circuit model.............. 170 8.3 Designing a two-cavity/one-qubit device.................... 171 8.3.1 Simulation and black-box quantization analysis............ 175 8.3.2 Transmon geometry............................ 176 v 8.4 Fabrication...................................... 176 8.5 Measurements.................................... 178 8.5.1 Spectroscopy and pulse tune-up..................... 181 8.5.2 Coherence times.............................. 182 8.5.3 Qubit anharmonicity and excited state population........... 184 8.5.4 Demonstration of strong dispersive regime cQED........... 184 8.5.5 Determination of cross-Kerr........................ 186 8.6 Discussion of loss mechanisms.......................... 187 8.6.1 The Purcell effect.............................. 187 8.6.2 Surface Losses................................ 189 8.6.3 Seam Losses................................. 190 8.6.4 Conductance discussion.......................... 194 8.7 Outlook........................................ 195 8.7.1 Increased coupling by etching...................... 196 8.7.2 Planar readout resonator.......................... 197 8.7.3 Conclusion................................. 199 9 Conclusion 200 9.1 Future Work..................................... 200 9.2 Conclusion...................................... 201 A Fabrication details 203 A.1 Recipes........................................ 204 A.2 Electroplating Indium............................... 207 A.2.1 Electroplating indium on wafers..................... 209 A.3 Indium Bump Literature Review......................... 211 A.4 Bonding....................................... 213 A.5 Josephson Junction fabrication.......................... 214 A.6 Surface roughness.................................