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Testing the Quantum-Classical Boundary and Dimensionality of Quantum Systems

Hou Shun Poh

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

No journey of scientific discovery is ever truly taken alone. Every step along the way, we encounter people who are a great source of encouragement, guidance, inspiration, joy, and support to us. The journey I have embarked upon during the course of this project is no exception. I would like to extend my gratitude to my project partner on many occasion during the past 5 years, Ng Tien Tjeun. His humorous take on various matters ensures that there is never a dull moment in any late night lab work. A resounding shout-out to the ‘elite ’ mem-bers of 0205 (our office), Tan Peng Kian, Shi Yicheng, and Victor Javier Huarcaya Azanon for their numerous discourses into everything under the sun, some which are possibly work related. Thank for tolerating my borderline hoarding behavior and the frequently malfunc-tioning door? I would like to thank Alessandro Ceré for his invaluable inputs on the many pesky problems that I had with data processing. Thanks for introducing me to world of Python programming. Now there is something better than Matlab? A big thanks also goes out to all of my other fellow researchers and colleagues both in the Quantum Optics group and in CQT. They are a source of great inspiration, support, and joy during my time in the

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For certain problems quantum resources can exponentially increase computing power, but these quantum resources are very fragile in practice. When a quantum system interacts with an external environment, it undergoes decoherence the loss of quantum correlation and relaxation the loss of energy and eventually all of the quantum information is lost. Here we show a general principle of using unitary operators to suppress relaxation processes. Unitary operations do not cool a quantum system and seem an unlikely candidate for preventing irreversible thermodynamic heating processes, but surprisingly most decoherence processes can be corrected or ameliorated using open loop control with unitary controllers. We examine the different mechanisms of decoherence and relaxation on simple spin systems and discuss when the modes can be corrected. We show experimentally the feasibility of our correction schemes using nuclear magnetic resonance. We also demonstrate control of the nuclear spins over long time scales. Finally, we discuss the applications of unitary correction to higher dimensional systems and the potential applications to quantum information processing. Thesis Supervisor: Neil Gershenfeld Title: Associate Professor Spingineering: Quantum Control in the Presence of Relaxation by Benjamin Harris Recht Submitted to the Media Arts and Sciences department in partial fulfillment of the requirements for the degree of Master of Science in Media Arts and Sciences at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2002 Thesis Advisor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neil Gershenfeld Associate Professor Department of Media Arts and Sciences Massachusetts Institute of Technology Thesis Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isaac Chuang Associate Professor Department of Media Arts and Sciences Massachusetts Institute of Technology Thesis Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seth Lloyd Professor Department of Mechanical Engineering Massachusetts Institute of Technology Acknowledgments This thesis, being no different than any other, would have not been possible without some truly remarkable people. I would like to thank my advisor Neil Gershenfeld for his support and guidance through my first two years and my readers: Isaac Chuang for introducing me to and guiding me through the quantum world, and Seth Lloyd for always saying just the right thing at the right time. I owe a large thank you to Yael Maguire for inspiring this work and his eagerness to discuss my progress. Thanks to Matthias Steffen and Yael for making sure that my theorist hands never broke the ever fussy 500 MHz NMR spectrometer. I would also like to thank Aram Harrow and Ali Rahimi for invaluable discussions and suggestions. Thanks to Jason Taylor for bearing with me in the confines of our office and to the rest of the PHM crew: Matt, Rehmi, Ben, Rich, Ravi, Bernd, John-Paul, Dan, Caroline, Esa, Femi. Thanks to Linda Peterson and Pat Sokaloff for taking extra time to care about all of us lost and helpless graduate students. I also owe a great deal of thanks to Susan MurphyBottari, Mike Houlilhan, and Liz Hennessey for making the PHM machine run as smoothly as it does. I send much love and respect to the unlockedgroove crew and all of the people who frequent to the Appliance of Science for helping me maintain my sanity. Thank you Mom and Dad for 24 years of constant support and Marissa for never forgetting to tell me when I’m wrong. Thank you Lauren for being exactly who you are. Thanks to the MIT Media Laboratory and the Things That Think Consortium. This thesis would not have been possible without the constant support of Nicotine, Caffeine, Alcohol, and Cholesterol. Thank you for better living through chemistry.

•Jan 1, 2002•1 citation
No journey of scientific discovery is ever truly taken alone. Every step along the way, we encounter people who are a great source of encouragement, guidance, inspiration, joy, and support to us. The journey I have embarked upon during the course of this project is no exception. I would like to extend my gratitude to my project partner on many occasion during the past 5 years, Ng Tien Tjeun. His humorous take on various matters ensures that there is never a dull moment in any late night lab work. A resounding shout-out to the ‘elite ’ mem-bers of 0205 (our office), Tan Peng Kian, Shi Yicheng, and Victor Javier Huarcaya Azanon for their numerous discourses into everything under the sun, some which are possibly work related. Thank for tolerating my borderline hoarding behavior and the frequently malfunc-tioning door? I would like to thank Alessandro Ceré for his invaluable inputs on the many pesky problems that I had with data processing. Thanks for introducing me to world of Python programming. Now there is something better than Matlab? A big thanks also goes out to all of my other fellow researchers and colleagues both in the Quantum Optics group and in CQT. They are a source of great inspiration, support, and joy during my time in the
A well isolated environment can be ideal for a quantum system to perform e ciently. Unlike this a PhD student needs to interact with many people during the course to complete a research project timely. Having said that, here is a list of people whom I would like to pay my deepest and profound gratitude. I would like to thank my rst principal supervisor Prof. David Kielpinski, who accepted me to work in his research group and guided me like a professional physicist. Later on, sudden news about his permanent departure to USA at the stage when I was really close to nish a project was quite challenging. Nevertheless, Dr. Erik Streed and Dr. Mirko Lobino took me under their wings as new advisers with their instrumental counselling to complete my PhD thesis. My special thanks goes to Dr. Tim Byrnes from New York University, with whom I did some theoretical work mentioned in the thesis. Beside these, my lab fellows including Matthew Petrasiunas, Valdis Blums, Paul Fisher, Dr. Ben Norton and Dr. Moji Ghadimi were very instructive and helping during my stay at Gri th University. Above all, I have no words to thank my parents and family for their selfess support over the years. An experimental research project is no more than a dream without money. Therefore, I would like to say a big thanks to all the funding agencies who were linked to this project, directly or indirectly from the beginning to end, including Gri th University for their international postgraduate research and postgraduate research scholarships, the US air force and the Australian research council.
6 years ago when I joined the group, Elaine gave me a lab tour. I saw Jun and Yanwen sitting in the dark and taking data. At that time there was a big chiller in the time domain lab and making huge noise. Frankly, I was a bit scared since I had never been in a real lab before graduate school. I was wondering whether I could do well in such a lab as an experimental physicist. Now it is 6 years later and I am so happy to say that I made it. During the entire graduate school, there are so many people I would like to thank. The first and the most important person I would like to thank is my advisor Professor Duncan Steel. I am so lucky to have Duncan as my advisor. He is such a smart scientist with great personality. His working ethics and conscientious attitudes inspired me a lot in research. He always tries to create the best education and research support for me. One of the greatest things is that he tried to develop my weakness, exploit my strength, and carefully shape me to be a good physicist. Duncan is also an advisor with a great sense of humor and it is so much fun to work with him. I would like to thank Professor Paul Berman. His lectures of quantum optics is
This thesis is dedicated to my dearest wife, Yingyan, who has been a constant source of inspiration and support through all stages of my life since high school, and to our lovely boy, Logan, who came to our family just before the thesis was finished. iv Acknowledgments First, I would like to thank my advisor Professor Jonas Zmuidzinas for giving me the opportunity to work on this great project of MKID. I came to Caltech in 2002 and originally planned to work in the field of optics. Failing to join any optics group on campus, I luckily ran across Jonas in a talk on MKID he gave to the students in applied physics major. These detectors made of resonators immediately attracted my interest. I still remember the interview that took place at Jonas ’ office. Desperate to join a research group, I was advertising how good I was in both theory and experiment. At some point I mentioned that I had taken a mathematical course on stochastic process, which had caught Jonas ’ attention. He immediately gave me a quiz, asking me to state the Weiner-Kinchin theorem. Fortunately, I was able to give the correct answer promptly. He was very satisfied and said, “Let me show you the lab.” That was how I joined the MKID group and also where my journey of noise study started. It
For certain problems quantum resources can exponentially increase computing power, but these quantum resources are very fragile in practice. When a quantum system interacts with an external environment, it undergoes decoherence the loss of quantum correlation and relaxation the loss of energy and eventually all of the quantum information is lost. Here we show a general principle of using unitary operators to suppress relaxation processes. Unitary operations do not cool a quantum system and seem an unlikely candidate for preventing irreversible thermodynamic heating processes, but surprisingly most decoherence processes can be corrected or ameliorated using open loop control with unitary controllers. We examine the different mechanisms of decoherence and relaxation on simple spin systems and discuss when the modes can be corrected. We show experimentally the feasibility of our correction schemes using nuclear magnetic resonance. We also demonstrate control of the nuclear spins over long time scales. Finally, we discuss the applications of unitary correction to higher dimensional systems and the potential applications to quantum information processing. Thesis Supervisor: Neil Gershenfeld Title: Associate Professor Spingineering: Quantum Control in the Presence of Relaxation by Benjamin Harris Recht Submitted to the Media Arts and Sciences department in partial fulfillment of the requirements for the degree of Master of Science in Media Arts and Sciences at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2002 Thesis Advisor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neil Gershenfeld Associate Professor Department of Media Arts and Sciences Massachusetts Institute of Technology Thesis Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isaac Chuang Associate Professor Department of Media Arts and Sciences Massachusetts Institute of Technology Thesis Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seth Lloyd Professor Department of Mechanical Engineering Massachusetts Institute of Technology Acknowledgments This thesis, being no different than any other, would have not been possible without some truly remarkable people. I would like to thank my advisor Neil Gershenfeld for his support and guidance through my first two years and my readers: Isaac Chuang for introducing me to and guiding me through the quantum world, and Seth Lloyd for always saying just the right thing at the right time. I owe a large thank you to Yael Maguire for inspiring this work and his eagerness to discuss my progress. Thanks to Matthias Steffen and Yael for making sure that my theorist hands never broke the ever fussy 500 MHz NMR spectrometer. I would also like to thank Aram Harrow and Ali Rahimi for invaluable discussions and suggestions. Thanks to Jason Taylor for bearing with me in the confines of our office and to the rest of the PHM crew: Matt, Rehmi, Ben, Rich, Ravi, Bernd, John-Paul, Dan, Caroline, Esa, Femi. Thanks to Linda Peterson and Pat Sokaloff for taking extra time to care about all of us lost and helpless graduate students. I also owe a great deal of thanks to Susan MurphyBottari, Mike Houlilhan, and Liz Hennessey for making the PHM machine run as smoothly as it does. I send much love and respect to the unlockedgroove crew and all of the people who frequent to the Appliance of Science for helping me maintain my sanity. Thank you Mom and Dad for 24 years of constant support and Marissa for never forgetting to tell me when I’m wrong. Thank you Lauren for being exactly who you are. Thanks to the MIT Media Laboratory and the Things That Think Consortium. This thesis would not have been possible without the constant support of Nicotine, Caffeine, Alcohol, and Cholesterol. Thank you for better living through chemistry.