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  • Single Electron Spin Qubits in Silicon

    Quantum Dots

    David Zajac

    A Dissertation

    Presented to the Faculty

    of Princeton University

    in Candidacy for the Degree

    of Doctor of Philosophy

    Recommended for Acceptance

    by the Department of


    Adviser: Jason R. Petta

    September 2018

  • c© Copyright by David Zajac, 2018.

    All rights reserved.

  • Abstract

    Electron spins in quantum dots form ideal two-level systems for implementing

    quantum computation in the solid state. While spin states can have extremely long

    quantum coherence times, addressing single spins and coupling large arrays of spins

    have been formidable experimental challenges. Research over the past several decades

    has resulted in a variety of creative approaches to address these problems, yielded new

    insights into the physics of spins in semiconductors, and demonstrated many of the

    basic criteria for quantum computation.

    This thesis presents a systematic study of the physics and quantum control of spins

    in few-electron Si/SiGe quantum dots. We present novel designs for quantum dot de-

    vices that yield improved control of single electron wavefunctions. We demonstrate

    full control of single electron spin states by placing a quantum dot in the vicinity of a

    strong magnetic field gradient produced by a micron-scale ferromagnet, and quantify

    the control fidelity using randomized benchmarking. Utilizing the exchange interac-

    tion between neighboring spins in combination with arbitrary single-spin rotations,

    we present one of the first demonstrations of all the criteria for universal quantum

    computation (initialization, readout, and a universal set of gates) with electron spins

    in a single device. Finally, we take the first steps towards controlling a large array of

    quantum dots by deterministically shuttling single electrons through an array of nine

    quantum dots.


  • Acknowledgements

    Firstly I would like to thank my advisor Jason Petta for all of the guidance he has

    provided over the course of my PhD. Throughout the years working in his lab I’ve

    learned an incredibly diverse set of skills including sweating copper pipes, designing

    printed circuit boards, fabricating nanoscale electronics, installing dilution refrigera-

    tors, manipulating microwave signals, and many more. Above all I’ve learned from

    Jason how to approach problems with intense focus and how to avoid getting dis-

    tracted from the big picture goal. I’ve learned by example how to give a good, clear

    presentation, how to get in the lab and make things happen, and the genius that is

    the Sawzall. I’m truly grateful for my experience in working in his lab and have no

    doubt that it will serve me well in the future.

    Throughout my time in Petta Lab I’ve been privileged to work alongside a great

    cohort of peers. Xiao Mi has demonstrated a truly impressive work ethic and an

    uncanny ability to plow through tough problems. George Stehlik has the ability to

    lift the spirits of those around him with a childish sense of wonder and playfulness,

    and I will miss racing him to the coffee machine after lunch each day. Ke Wang

    really helped me get started in the lab and passed on indispensable knowledge of

    the cleanroom that was key to my success within the group. Peace always impressed

    me with his efficiency and ingenuity in the lab. For someone so quiet in lab, I

    was amazed by Yinyu’s ability to relentlessly churn out new results. Tom Hazard

    always lightened the mood around the lab, and has been great to have as a climbing

    partner and friend. Stefan Putz always kept the lunchtime discussions interesting

    with intriguing trivia. Felix Borjans and Adam Mills have both impressed me with

    their programming skills, and I have no doubt the lab will be in good hands with

    them alongside the experimental expertise of Anthony Sigillito.

    I also could not have done the work in this thesis without the support of our

    collaborators. Jake Taylor and Guido Burkard provided invaluable theory support


  • while exploring the exchange interaction between neighboring spins. Max Russ and

    Michael Gullans have both been extremely patient in explaining new theory concepts

    to me. Also, none of this could have been possible without financial support from

    agencies that fund our research. The work in this thesis was supported by US Depart-

    ment of Defense under contract H98230-15-C0453, the Army Research Office through

    Grant No. W911NF-15-1-0149, the Gordon and Betty Moore Foundations EPiQS Ini-

    tiative through grant GBMF4535, the National Science Foundation through Grants

    No. DMR-1409556 and No. DMR-1420541, and the Spanish Ministry of Economy

    and Competiveness through Grant MAT2017-86717-P. Also, the devices these ex-

    periments were performed on were fabricated in the Princeton University Quantum

    Device Nanofabrication Laboratory.

    I’ve also had the support of numerous friends and family members over the span

    of my PhD. I wish I could thank you all individually, but know that even if you’re not

    mentioned here I appreciate everything that you’ve done for me over this significant

    period of my life. Throughout my time at Princeton I could always count on Zach

    Sethna to get me out of the lab to play softball, get in a quick game of pool between

    study sessions, or host a night of drinks at the Z-bar. As for Josh Hardenbrook, I’ll

    always remember our Monday night fantasy league, you forcing me to go to the gym

    at unreasonable hours, and your intense drive for life.

    Life at Princeton would not have been what it was without KL by my side. You’ve

    been so supportive throughout this entire process and have helped me grow as a

    person. I’m excited to move to NYC with you and start a new chapter in our lives

    which I’m sure will be every bit as special as our time together in Princeton. Robin

    and Michelle, you’ve treated me like family and given me a home away from home,

    and I can’t say how grateful I am for that. The number of ways you’ve helped me

    over the years is immeasurable, but if it could be measured I have a feeling it would

    be in six-packs and racks of ribs. Dick and Mo, you’ve also become family to me, and


  • taught me some of the best jokes I know. Mattia I’ve felt like a brother with you,

    sharing apartments over the past few years. Princeton doesn’t feel the same without

    you, and I hope you’ll move back to the east coast once you get fed up with the San

    Fransisco weather. Leslie, I can always count on you to make me smile. Spending

    time with you always reminds me of what’s most important in life.

    Of course the people who have most shaped who I am throughout my life is my

    family. Tommy, I couldn’t have asked for a better brother in life. Thank you for

    supporting me from all the way across the country. Whether it’s airport phone calls,

    late night gaming, or family vacations, it’s always great to spend time with you. Aunt

    Noreen, you’ve also been a big part of my life for as long as I can remember. As a

    kid I remember always being excited to spend the day with Aunt Noreen and that’s

    still true to this day.

    Lastly, no one has supported me more than my parents. Dad, thanks for inspiring

    my passion for building things with my own hands. From constructing skateboard

    ramps to pool decks, watching and learning from you has shaped the way I approach

    problems and came in handy during my research. Mom, probably no one has impacted

    who I am more than you. You’ve always encouraged me to pursue my interests and

    supported me in my pursuit. Whether it was driving me to hockey practice or signing

    me up for guitar lessons, you’ve always been there for me. Thanks Mom and Dad for

    making all of this possible. I couldn’t have done it without you.


  • The work described in this dissertation has been published in the following articles

    and presented at the following conferences:

    Appl. Phys. Lett. 106, 223507 (2015).

    Phys. Rev. Appl. 6, 054013 (2016).

    Science 359, 439 (2018).

    Nature 555, 599 (2018).

    American Physical Society Meeting, March 2015, San Antonio, Texas.

    Silicon Quantum Electronics Workshop, August 2015, Takamatsu, Japan.

    MRS Fall Meeting, November 2016, Boston, Massachusetts.

    American Physical Society Meeting, March 2017, New Orleans, Louisiana.

    Silicon Quantum Electronics Workshop, August 2017, Hillsboro, Oregon.

    Spin Qubit 3, November 2017, Sydney, Australia.

    American Physical Society Meeting, March 2018, Los Angeles, California.


  • Contents

    Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

    Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

    List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

    List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

    1 Introduction 1

    1.1 Quantum Computing . . . . . . . . . .