ABSTRACT Title of Dissertation: SCALING QUANTUM COMPUTERS WITH LONG CHAINS OF TRAPPED IONS Laird Nicholas Egan Doctor of Philosophy, 2021 Dissertation Directed by: Professor Christopher Monroe Department of Physics Joint Quantum Institute Quantum computers promise to solve models of important physical processes, optimize complex cost functions, and challenge cryptography in ways that are in- tractable using current computers. In order to achieve these promises, quantum computers must both increase in size and decrease error rates. To increase the system size, we report on the design, construction, and oper- ation of an integrated trapped ion quantum computer consisting of a chain of 15 171Yb+ ions with all-to-all connectivity and high-fidelity gate operations. In the process, we identify a physical mechanism that adversely affects gate fidelity in long ion chains. Residual heating of the ions from noisy electric fields creates decoherence due to the weak confinement of the ions transverse to a focused addressing laser. We demonstrate this effect in chains of up to 25 ions and present a model that ac- curately describes the observed decoherence. To mitigate this noise source, we first propose a new sympathetic cooling scheme to periodically re-cool the ions through- out a quantum circuit, and then demonstrate its capability in a proof-of-concept experiment. One path to suppress error rates in quantum computers is through quantum error correction schemes that combine multiple physical qubits into logical qubits that robustly store information within an entangled state. These extra degrees of freedom enable the detection and correction of errors. Fault-tolerant circuits contain the spread of errors while operating the logical qubit and are essential for realizing error suppression in practice. We demonstrate fault-tolerant preparation, measure- ment, rotation, and stabilizer measurement of a distance-3 Bacon-Shor logical qubit in our quantum computer. The result is an encoded logical qubit with error rates lower than the error of the entangling operations required to operate it. Scaling Quantum Computers with Long Chains of Trapped Ions by Laird Nicholas Egan Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2021 Advisory Committee: Professor Christopher Monroe, Chair/Advisor Professor Norbert Linke Professor Alicia Koll´ar Professor Vladimir Manucharyan Professor Christopher Jarzynski c Copyright by Laird Nicholas Egan 2021 Acknowledgments I will start by acknowledging that I was not a typical physics graduate student, since my previous 5 years were spent in industry working for a defense contractor. It is not lightly that one makes the decision to leave a well-paying career to pursue cutting-edge academic research with its long hours and often thankless work. I am very thankful to my co-workers Dave Coar, Manny Stockman, and Brian Holloway, who helped me to kick the idea around my head, set expectations on the experience, and have remained in touch throughout my entire journey. On the other side of the fence, I am very thankful to my advisor, Chris Monroe, who took a bit of a risk on my non-traditional resume, unsure of how I would perform in an academic setting. He still welcomed me with open arms even after I told him that I wanted to graduate in 4 years and then immediately return to industry. Throughout the entire experience, he has always been supportive of my ambitions and an amazing resource for physics and career advice. One of my goals when starting this journey, was that I wanted to be surrounded by the best and the brightest in the field. I found it in Marko Cetina, who led the experiment with wisdom, insight, and tenacity from when I arrived to the day I started writing this thesis. I also had the opportunity to work alongside several other extremely talented and creative post-docs in Kristi Beck, Michael Goldman, and Crystal Noel. I am especially grateful for Kristi, who took me under her wing when I first joined and put up with a lot of stupid questions while I learned the ropes. I also had the pleasure of spending many days in the lab with Drew Risinger, ii Daiwei Zhu, Debopriyo Biswas, and Bahaa Harraz. Physics is a team sport and I could not have done it without your skills and good humor. I would also like to thank Jonathan Mizrahi, Kai Hudek, and Jason Amini, who designed the system before I arrived and encapsulated the proverb of planting trees in whose shade they shall never sit. Finally, I need to thank all of the remaining members of Chris's lab, of which there are too many to enumerate, but who I shared many great conversations and friendships with over lunch or the espresso machine. Perhaps the most rewarding experience throughout my journey was the amaz- ing collaboration I had with Ken Brown's group on our joint quantum error-correction results. Far be it from the head in the clouds stereotype of theorists, Ken was al- ways willing to jump into the nitty-gritty of our machine and to adjust his ideas to meet us half-way, often resulting in spectacular data. I also had the pleasure of working closely with one of Ken's students, Dripto Debroy, who I shared the pain of writing multiple papers with and made calculating IARPA benchmarks an enjoy- able experience. The rest of the theory team at Duke, including Michael Newman, Muyuan Li, James Leung, and the experimental team of Jungsang Kim, including Stephen Crain and Ye Wang were critical resources and fruitful partners on the IARPA LogiQ program. My family has been an amazing support structure throughout this journey. I cannot articulate how grateful I am to my parents Dave and Tina, for instilling an intellectual curiosity in me and for enthusiastically following every development in my adventure. My brother, Garth, paved the way for doctoral degrees at UMD and was a great source of commiseration. My sister, Tessa, is an unbounded source of iii inspiration and joy. I was very fortunate to pursue my degree near my in-laws, Jim, Amy, and Grace who provided many hot meals while I worked late nights and were always eager to hear another explanation of quantum computing. Saving the best for last, I could not have done this without my incredible wife Liz. She was fully on-board with the concept that we may have to move across the country and find her a new job, just so I could take a pay-cut and work long hours. Her support has never wavered from that moment. Thank you for walking next to me on this fantastic journey we call life. iv Table of Contents Acknowledgements ii Table of Contentsv List of Tables viii List of Figures ix List of Abbreviations xi 1 Introduction1 1.1 Quantum Computers...........................1 1.2 Trapped Ion Quantum Computers....................4 1.3 Thesis Outline...............................7 2 Trapped Ion Basics8 2.1 Ion Traps.................................8 2.1.1 Linear RF Paul Trap.......................9 2.1.2 Micro-fabricated Surface Traps................. 13 2.1.3 Ion Crystals and Normal Modes................. 16 2.2 The 171Yb+ Ion.............................. 25 2.2.1 Ionization and Loading...................... 28 2.2.2 Doppler Cooling.......................... 30 2.2.3 State Preparation......................... 34 2.2.4 State Detection.......................... 36 2.2.5 The 171Yb+ Hyperfine Structure................. 38 3 From Ions To Qubits 42 3.1 Coherent Raman Control......................... 42 3.1.1 Simple Trapped Ion Model.................... 43 3.1.2 Raman Transitions........................ 47 3.1.3 Raman Frequency Combs.................... 52 3.1.4 Four-Photon Stark Shifts..................... 58 3.2 Digital Single Qubit Gates........................ 62 3.3 Digital Two Qubit Gates......................... 65 3.3.1 Mølmer-Sørensen Interaction................... 67 v 3.3.2 AM Laser Pulse Shaping..................... 74 3.3.3 Linearly Interpolated Gate Solutions.............. 78 3.3.4 Optimizing Gates for Robustness................ 86 4 Integrated Ion Trap System 90 4.1 Vacuum Chamber Subsystem...................... 92 4.2 Trap Subsystem.............................. 95 4.2.1 Sandia HOA 2.1.1......................... 95 4.2.2 RF Resonator........................... 98 4.2.3 DC Voltage Controller...................... 100 4.3 CW Laser Subsystem........................... 101 4.4 Raman Subsystem............................ 103 4.4.1 Rep Rate Control and Stabilization............... 106 4.5 Imaging Subsystem............................ 108 4.6 Control Subsystem............................ 111 4.6.1 Main Control Subsystem..................... 112 4.6.2 Coherent RF Control Subsystem................ 113 5 System Operation, Calibration, and Characterization 116 5.1 System Operation............................. 116 5.1.1 Autoloading Ions......................... 116 5.1.2 Ground State Cooling...................... 118 5.1.3 Ion-based Beam Pointing Lock.................. 120 5.2 System Calibration............................ 121 5.2.1 Nulling Stark Shifts via Laser Repetition Rate......... 121 5.2.2 Voltage Calibrations....................... 126 5.2.3 Gate Calibrations......................... 128 5.3 System Characterization......................... 130 5.3.1 State Preparation And Measurement Error........... 130 5.3.2 Rabi Crosstalk.......................... 132 5.3.3 Single Qubit Gate Performance................. 137 5.3.4 Two Qubit Gate Performance.................. 138 5.3.5 Anomalous