\chapter{Acknowledgements}

Venturing into the research frontier of quantum engineering truly gives me an exciting sense of satisfaction, especially when our research becomes directly relevant to the scientific community in their quest towards the unknown.
This opportunity could not be made possible for me without my respectable supervisor, Prof. Matthias Troyer.
His ambient guidance has cultivated both my thinking and knowledge over these years, and I am deeply influenced by his humble character in the acquisition of knowledge.
I have benefited tremendously from his vast experience in computer science, particularly in appreciating the art of modern programming.
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\noindent An equivilently important person who has influenced my life is my former supervisor, Prof. Fu Chun Zhang.
Perhaps my interest for strongly correlated physics started with his motivating lectures on quantum mechanics during my undergraduate studies.
Indebted to his generous opportunity to send me here at ETH Zurich in 2006,  my entire vision of numerics and scientific computing had since widened and resulted in my love for them.
Without his support all these years, I would not be whom I am today. 
Here, I want to reemphasize my appreciation for him as my role model in scientific research.
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\noindent Special appreciation is given to my closest collaborators: Prof. Lode Pollet, who selflessly imparts the essence of QMC directed wom algorithm to me; and Dr. Sebastiano Pilati, who shares his vast knowledge in diffusion Monte Carlo with me. 
Special thanks are given to Prof. Xi Dai who shares with me his experience of working with DFT electronic structure calculations.
Not to forget my bosonic collaborators in the earlier days, who include Prof. Daw-Wei Wang, Prof. Po-Chung Chen, Shiang Fang, and Chia-Ming Chung.
Fruitful discussions with Prof. T-L. Ho, and Dr. Qi Zhou, on thermometry concepts; Prof. Phillip Werner, Prof. Takashi Oka, Dr. Naoto Tsuji, and Dr. Lei Wang, on diagrammatic corrections beyond DFT, are deeply appreciated.
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\noindent Academic visits cannot be made possible without certain important people.
I would like to express my deepest gratitudes to Prof. Immanuel Bloch for inviting me to the Max Planck Institute, Prof. Hideo Aoki to Tokyo University, Prof. Fu Chun Zhang to Hong Kong University, Prof. Xi Dai to the Chinese Academy of Science, Prof. Daw-Wei Wang to the National Center for Theoretical Sciences of Taiwan, and Prof. Jian-Sheng Wang to the National University of Singapore.
Special thanks are also given to Prof. Dielthem Wurtz for inviting me twice to his financial engineering workshop in Meielisalps, whom I met there Dominik Locher and Yangyang.
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\noindent Sincere gratitudes are expressed to my German tutors, Paulina Velasco, Andreas Hehn, and Lea Kraemer (in addition for her help with the Zusammenfassung in this thesis).
In addition, Dr. Phillip Carboz, Dr. Bela Bauer, Jan Gukelberger, and Michele Dolfi have helped me a lot with administrative issues that pop up unexpectedly during my academic research.
It is worth also mentioning Dr. Zhenya Kozik, Dr. Juan Carlos, and Dr. Peter Anders for bringing so much fun to my research in the earlier days.
Here, I want to express my thanks to all present colleagues at ETH Zurich, as well as all former colleagues at Hong Kong University, for shaping me into whom I am today.
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\noindent This scientific research can not be possible with the funding from Swiss National Foundation and ETH Zurich.
Besides, I must also thank the Brutus cluster of ETH Zurich as well as its support team for working so hard for my project with thousands of CPU processors. 
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\noindent Last but not least, I have to express my gratitude to my parents who gave me such wonderfully intelligent genes.
Their love and support have always been with me since my very first day on Earth.
And how could I dare to forget you, Yangyang, the only one whom I love most?
Yes, that's right!
You are most appreciated. 