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Does Richard Feynman Dream of Electric Sheep? Topics on Quantum Field Theory, Quantum Computing, and Computer Science

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Does Richard Feynman Dream of Electric Sheep? Topics on Quantum Field Theory, Quantum Computing, and Computer Science Does Richard Feynman Dream of Electric Sheep? Topics on Quantum Field Theory, Quantum Computing, and Computer Science Thesis by Junyu Liu In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2021 Defended May, 3, 2021 ii © 2021 Junyu Liu ORCID: 0000-0003-1669-8039 All rights reserved except where otherwise noted iii ACKNOWLEDGEMENTS Caltech is really an amazing school with an excellent academic environment. I am very lucky to have been here to receive so many educational opportunities, collaborations, and friendships. As a starting point of my professional career, I am trying to be a theoretical physicist, a dream I have had from childhood. It has also provided me an excellent platform to interact with great minds not only inside the campus, but also the whole high energy physics and quantum information science community. These important five years are treasures in my whole life. Firstly, I wish to thank my advisors. I am lucky enough to be advised by three great scientists at the same time, Clifford Cheung, John Preskill, and David Simmons- Duffin, (listed in the alphabetical order). They are great academic advisors, encour- aging me to solve important scientific problems, and giving me infinite suggestions about science and careers during my hard time. Cliff is really a hero. I will remember infinite discussions we had on the fourth floor of Downs-Lauritsen, or under the beautiful sunshine of Pasadena. For me, Cliff is a great mentor, teacher, and friend both in my academic and personal life. From him, I learned how to dive into problems deeply and think about important problems, and also be active on exploring different scientific problems and their intersections. I believe those exceptional insights and profound knowledge will benefit me throughout my life. For me, John is one of the most outstanding wise men of our time, and it has been my great honor to interact and work with him. When I was looking for research opportunities as a young graduate student, John brought a fascinating world, quantum information science, to me. What I have learned the most from him is to consider the long-term impact when choosing a research topic. As a great mentor, John is very considerate and full of patience, of which I will have a lasting memory. David is a legend in theoretical physics. Working with David is a fantastic ex- perience. When I ask David questions, he can remember almost everything and write a crystal-clear explanation on the blackboard, including complicated series of conformal block expansions. At the same time, David is also an excellent friend, and I am very thankful for his tolerance of my jokes, the outstanding organization of the bootstrap collaboration, and the Caltech conformal group. iv To continue, I wish to thank other collaborators during my graduate school: Ning Bao, Alexander Buser, Shai Chester, Jordan Cotler, Hrant Gharibyan, Masanori Hanada, Masazumi Honda, Nicholas Hunter-Jones, Per Kraus, Walter Landry, Aitor Lewkowycz, Tianlin Li, Yue-Zhou Li, Don Marolf, David Meltzer, Ashley Milsted, Eric Perlmutter, David Poland, Grant Remmen, Vladimir Rosenhaus, Eva Silver- stein, Ning Su, Jinzhao Sun, Gonzolo Torroba, Alessandro Vichi, Guifre Vidal, Yuan Xin, Beni Yoshida, Xiao Yuan, Qi Zhao, Yehao Zhou, and You Zhou. Working with all of you has given me excellent and unforgettable memories! I also wish to thank many other physics or STEM colleagues for your discussions and friendships: Soner Albayrak, Victor Albert, Mustafa Amin, Guy-Gur Ari, Nima Arkani-Hamed, Yimu Bao, Yoni Bentov, David Berenstein, Dominic Berry, Fernando Brandao,˜ Charles Cao, Marcela Carena, Sean Carroll, Xie Chen, Gong Cheng, Andrew Childs, Soonwon Choi, Clay Cordova, William Cottrell, Elizabeth Crosson, Bartek Czech, Alex Dalzell, Maria Derda, Xi Dong, Rajeev Erramilli, Bradley Filippone, Liam Fitzpatrick, Weibo Fu, Andras Gilyen, Victor Gorbenko, Yingfei Gu, Charles Hadfield, Nicole Yunger Halpern, Connor Hann, Daniel Har- low, Jim Hartle, Tom Hartman, Patrick Hayden, Hong-Ye Hu, Yangrui Hu, Robert Huang, Alexander Jahn, Liang Jiang, Zhang Jiang, Denis Karateev, Kohtaro Kato, Emanuel Katz, Isaac Kim, Alexei Kitaev, Natalie Klco, Murat Kologlu, Shota Ko- matsu, Grisha Korchemsky, Petr Kravchuk, Richard Kueng, Henry Lamm, Adam Levine, Zhijin Li, Ying-Ying Li, Shu Lin, Ying-Hsuan Lin, Hong Liu, Jiahui Liu, Peter Love, Andreas Ludwig, Matilde Marcolli, Antonio Mezzacapo, Spiros Micha- lakis, Alexey Milekhin, Ryan Mishmash, Evgeny Mozgunov, Sepehr Nezami, Hirosi Ooguri, Sam Pallister, Julio Parra-Martinez, Fernando Pastawski, Geoffrey Pening- ton, Xiao-Liang Qi, Daniel Ranard, Sam Roberts, Junchen Rong, Slava Rychkov, Subir Sachdev, Burak Şahinoğlu, Prashant Saraswat, Martin Savage, Steve Shenker, Gary Shiu, Ashmeet Singh, Ronak Soni, Jon Sorce, Douglas Stanford, Leo Stein, Alexandre Streicher, Yuan Su, Jiarui Sun, Chong Sun, Brian Swingle, Eugene Tang, Aron Wall, Tian Wang, Wanchun Wei, Mark Wilde, Mark Wise, Zhong-Zhi Xianyu, Dan Xie, Hao-Lan Xu, Xi Yin, Yi-Zhuang You, Ellis Ye Yuan, Pengfei Zhang, Shangnan Zhou, and Sisi Zhou. Furthermore, I wish to thank so many wonderful places I’d had the chance to visit: Stanford (thanks Xiao-Liang Qi and Eva Silverstein for hosting), UCSB/KITP (thanks Don Marolf for hosting), UCSD (thanks Yi-Zhuang You for hosting), UC Berkeley (thanks Soonwon Choi for hosting), Fermilab, University of Chicago, v University of Colorado Boulder, Princeton, IAS, Harvard, MIT, ··· , partially with the help of the Simons collaborations on "It from Qubit" and "the Nonperturbative Bootstrap", QOALAS collaboration, and the MURI collaboration on "Quantum Codes, Tensor Networks, and Quantum Spacetime." I also wish to thank the IAS summer school, TASI summer school, PsiQuantum Corporation for their study and internship opportunities in Summer 2018, 2019, and 2020 respectively. I wish to thank all my friends during my graduate school, especially Wen-Loong Ma for his efficiency on eating, Honglie Ning for his driving skill, Burak Şahinoğlu and Eugene Tang for some dark secrets about clubs, Weibo Fu, Masanori Hanada, Zhe Jia, Xiang Li, David Meltzer, Ashley Milsted and Yehao Zhou for their long- lasting friendship and help, Xinyue Dai, Nicole Jinglin Gao for her paintings, and Rui Niu, Linrui Xiong for her arts. Moreover, I wish to thank all my IQIM friends, quantum information friends, Downs-Lauritsen fourth floor friends, high energy friends, physics friends, and other friends during my graduate study. I also wish to thank my friends who interact with me in the Los Angeles local organizations, including Animals, Anime, Cats, Film, Hanfu, and Rave. Thank you, Carol Silberstein, for your hard work in the Downs-Lauritsen fourth floor; Mika Walton and Marcia Brown, for your hard work on my student fairs; and Laura Kim, Daniel Yoder, for your hard work about international students like me. Thank you Ryan Patterson for being my committee chair and making me suggestions about cyberpunk. I wish to thank the University of Science and Technology of China, the Hong Kong University of Science and Technology, Nanjing University, Mcgill University and my undergraduate mentors, especially Robert Brandenberger, Yi-Fu Cai, Gang Chen, Henry Tye, and Yi Wang, who educated me as an undergraduate student and brought me to the path of graduate study. Finally, I wish to thank my cat Pafu for her lovely face. I wish to thank my father An Liu my mother Li Ren and my grandmother Soqiong Zeng for their infinite amount of financial and emotional support. vi ABSTRACT In this thesis, we mainly discuss three topics in theoretical physics: a proof of the weak gravity conjecture, a basic statement in the string theory landscape using the black hole entropy, solving the critical O¹3º model using the conformal boot- strap method involving semidefinite programming, and numerical simulation of the false vacuum decay using tensor network methods. Those topics cover different approaches to deep understanding of quantum field theories using concepts and methods of information theory, and computer science with classical and quantum computations. vii PUBLISHED CONTENT AND CONTRIBUTIONS This thesis contains the following three scientific publications. C. Cheung, J. Liu and G. N. Remmen, Proof of the Weak Gravity Conjecture from Black Hole Entropy, JHEP 10, 004 (2018), arXiv:1801.08546 [hep-th]. J. Liu participated in the conception of the project and the writing of the manuscript, deriving a general formula between the extremal condition and Wald entropy and applying the symbolic algebra on generalization to higher dimensions, and the writing of the manuscript. S. M. Chester, W. Landry, J. Liu, D. Poland, D. Simmons-Duffin, N. Su and A. Vichi, Bootstrapping Heisenberg Magnets and their Cubic Instability, arxiv: 2011.14647 [hep-th]. J. Liu participated in the conception of the project, the writing of the manuscript, and the organization of the collaboration, applying and strengthening the island and the OPE scan algorithm of the conformal O¹3º model, applying the sym- bolic algebra to deriving crossing equations with symmetries, and searching for the critical gap with dynamical algorithms. A. Milsted, J. Liu, J. Preskill and G. Vidal, Collisions of false-vacuum bubble walls in a quantum spin chain, arXiv: 2012.07243 [quant-ph]. J. Liu participated in the conception of the project, including numerical simula- tions on the dynamical evolution and entanglement/energy flux determination of the kink scattering process using software, as well as the writing of the manuscript. viii TABLE OF CONTENTS Acknowledgements . iii Abstract . vi Published Content and Contributions . vii Table of Contents . viii List of Illustrations . xi List of Tables . xxi Chapter I: Introduction: aspects of "cyberpunkian" quantum field theory . 1 1.1 Space opera and Cyberpunk . 1 1.2 Quantum field theory . 5 1.3 Simulating quantum field theory using quantum devices . 9 1.4 Conformal field theory and large-scale optimization . 12 1.5 The theoretical landscape and data science .
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