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.
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.
With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.
Precisely characterizing and controlling the dynamics of realistic open quantum systems has emerged in recent years as a key challenge across contemporary quantum sciences and technologies, with implications ranging from physics, chemistry and applied mathematics to quantum information processing (QIP) and quantum engineering. Quantum control theory aims to provide both a general dynamical-system framework and a constructive toolbox to meet this challenge. The purpose of this special issue of Journal of Physics B: Atomic, Molecular and Optical Physics is to present a state-of-the-art account of recent advances and current trends in the field, as reflected in two international meetings that were held on the subject over the last summer and which motivated in part the compilation of this volume—the Topical Group: Frontiers in Open Quantum Systems and Quantum Control Theory , held at the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP) in Cambridge, Massachusetts (USA), from 1–14 August 2010, and the Safed Workshop on Quantum Decoherence and Thermodynamics Control , held in Safed (Israel), from 22–27 August 2010. Initial developments in quantum control theory date back to (at least) the early 1980s, and have been largely inspired by the well-established mathematical framework for classical dynamical systems. As the above-mentioned meetings made clear, and as the burgeoning body of literature on the subject testifies, quantum control has grown since then well beyond its original boundaries, and has by now evolved into a highly cross-disciplinary field which, while still fast-moving, is also entering a new phase of maturity, sophistication, and integration. Two trends deserve special attention: on the one hand, a growing emphasis on control tasks and methodologies that are specifically motivated by QIP, in addition and in parallel to applications in more traditional areas where quantum coherence is nevertheless vital (such as, for instance, quantum control of chemical reactions or high-resolution magnetic resonance spectroscopy); on the other hand, an unprecedented demand for close coupling between theory and experiment , with theoretical developments becoming more and more attuned to and driven by experimental advances as different quantum technologies continue to evolve at an impressive pace in the laboratory. Altogether, these two trends account for several of the recurrent themes in this volume, as well as in the current quantum control literature as a whole: namely, the quest for control strategies that can attain the highest degree of precision and robustness possible, while striving for efficiency and, ultimately, optimality in achieving the intended control task under realistic operational constraints. From a theory standpoint, this makes it imperative to take into account increasingly more realistic control settings; to assess the quantitative impact of limited control resources and/or system knowledge; and to provide a rigorous and general foundation for existing experimental approaches in order to further enhance applicability and performance. From an experimental standpoint, renewed emphasis is in turn placed on validating theoretical predictions and benchmarking performance, so that the limiting constraints can be singled out for additional theoretical analysis and guidance. This ongoing cross-talk is clearly reflected in this collection, which brings together theoreticians and experimentalists, with a significant fraction of the papers reporting on combined quantum control theory–experiment efforts. While a precise categorization would neither be possible nor desirable, contributions to this volume have been loosely grouped into five broad sections. This grouping has been made in the hope that connections between different problems and/or technical approaches will become more transparent, facilitating the transfer of concepts and methods. The special issue opens with a section devoted to open-loop control methods, with special emphasis on dynamical decoupling (DD), which is becoming an increasingly important tool for decoherence control at the physical 'quantum firmware' level. In addition to including original research results, the first two articles, by Brion et al and Biercuk et al , also serve to pedagogically review some background in their respective subjects. In particular, Brion et al revisit one of the conceptually simplest approaches to open-loop manipulation of both closed and open quantum systems, nonholonomic control , motivated by its broad applicability to QIP settings. A special instance of open-loop control based on sequences of (nearly) instantaneous `bang-bang' pulses is addressed by Biercuk et al , who reformulate the simplest DD scenario, suppression of phase decoherence in a single qubit, as a filter-design problem. Peng et al report on the implementation of 'concatenated' DD for arbitrary single-qubit decoherence in the context of nuclear magnetic resonance QIP. A dedicated analysis of the performance of different DD schemes in the presence of realistic pulse errors is given by Wang and Dobrovitski. DD is also one of the strategies used by Lucamarini et al to reduce polarization decoherence in a photon qubit. These authors additionally report on the use of active feedback to counter transmission noise, effectively setting the stage for the second section, which is centered on closed-loop control. Unlike in open-loop control, measurement is an essential ingredient in closed-loop schemes aimed at both reliably identifying features of the target quantum system and further modifying its dynamics. The importance of directly measuring the spectrum of the underlying system-environment coupling is stressed by Almog et al , who show how this knowledge is crucial, in particular, for predicting the performance of DD sequences in experiments and for optimizing performance. Riofrio et al address a weak-measurement protocol for implementing quantum state tomography , which is a necessary 'primitive' for inferring the target quantum state and thereby diagnosing the control performance. Next, the impact of realistic control and system imperfections in continuous-time Markovian feedback strategies for rapid state preparation is analyzed by Combes and Wiseman. A prominent role is played in the special issue by optimal control (OC) approaches, reflecting their central importance for quantum control and QIP. The OC contributions have been divided into two separate sections, depending on whether the target dynamics is modeled as Hamiltonian (section 3) or dissipative (section 4), respectively. The contribution by Beltrani et al deals with `control landscapes', which provide a foundation for analyzing the performance of numerical OC algorithms and their robustness against control errors. Specifically, this paper characterizes geometric properties of the control landscape, relevant to the optimal control of state-to-state transitions. Application of OC theory to the problem of population transfer and coherence enhancement in Λ-systems is studied by Kumar et al , whereas Goerz et al report on the OC-design of a high-fidelity controlled phase-gate in atomic qubits. The robustness of an OC solution is specifically addressed by Negretti et al , along with an approach for identifying easily implementable while still 'close-to-optimal' control pulses. Powerful relaxation-optimized OC schemes (based on so-called opengrape algorithms) for generating unitary target gates in the presence of known dissipation parameters are discussed by Schulte-Herbrüggen et al . Next, Lapert et al report on the problem of time-optimal control of spin-1/2 systems undergoing Bloch relaxation dynamics, highlighting the crucial role played by singular extremals in the control synthesis. Alternative approaches for optimized control of qubits exposed to various decoherence processes are developed by Esher et al and Xue et al , based on a perturbative 'bath-optimized' formalism and on numerical optimization via a genetic algorithm, respectively. Testifying to the richness of the field, the volume concludes with four contributions that address a diverse range of problems. The exploitation of properties of adiabatic quantum evolutions is common to the first two papers. In particular, Legthtas et al offer a rigorous explanation for the robustness of a control protocol, chirped pulsing , that is widely employed in 'adiabatic rapid passage' experiments, while Han et al present a theoretical framework for adiabatic Raman photo-association schemes relevant to ultracold atomic systems. In the context of cavity quantum electrodynamics, Montenegro and Orszag describe how to engineer a system of two atoms coupled to distant lossy cavities so that stable atomic entanglement is generated. Finally, still very little is known about the physical mechanisms that are responsible for and control the experimentally observed 'coherent' features of transport phenomena in biological systems. The last contribution by Alicki and Giraldi analyzes energy transport in dynamical systems that can be modeled as 'quantum networks', and points to this fascinating emerging frontier. It is our hope that the above papers may help readers to gain an overview of some of the main trends in current quantum control efforts, both theoretical and experimental. In closing, we take the opportunity to thank the organizations which sponsored the above-mentioned ITAMP Topical Group (the United States National Science Foundation and Harvard University) and the Safed Workshop (the Israeli Science Foundation, the Safed Scientific Workshop program, CECAM and ACAM). Last but not least our sincere gratitude goes to all of the contributors to the volume and the reviewers as well as the J. Phys. B staff, for their respective efforts in preparing the papers and ensuring the overall quality of this special issue.
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
Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving small-scale demonstrations of quantum information processing. This was in large part made possible by the sophisticated methods of quantum control that have been developed by the NMR community over a span of more than 50 years. The traditional control methods, already perhaps the most complex examples of open-loop control available, were nevertheless designed primarily to assist in identifying the physical parameters of the underlying spin system, rather than to control the system with high precision. We have therefore extended the traditional methods in a variety of ways so as to achieve precise control, by taking advantage of prior knowledge of the physical parameters as determined by traditional methods. Due to the experimental challenges of real-time control, these developments relied upon our ability to simulate the evolution of the system under the action of radio-frequency control fields with essentially arbitrary precision, subject only to the available computing power. This talk presents an overview of our work in quantum control together with some of the on-going challenges still facing us
The development of quantum electrodynamics (QED), which studies the light-matter interaction in quantum level, has been accompanied by the enhancement of the coupling strength g between an atom (matter) and an electromagnetic (EM) field (light).With the introduction of a cavity, forming a cavity QED system, the coupling strength reached weak coupling (WC) and strong coupling (SC) regime.These regimes are defined by the system dissipations, the atom decay rate γ and the cavity decay rate κ, where g ≪ γ, κ for the WC regime and g ≫ γ, κ for the SC regime.Especially for the SC regime, the energy exchange between the atom and the EM field can happen repeatedly before the system losses the energy.This physical property enables quantum state manipulation in First and foremost, I would like to express my sincere appreciation to my principal supervisor, Takao Aoki, for his advice and support during my PhD studies.He is the first person who welcomed me to the field of cavity quantum electrodynamics at the end my third-year as an undergraduate student.Then, when I proposed to go to NICT and study about circuit QED and USC/DSC regimes, he agreed and quickly worked on the joined research contract, which yield the contents of this thesis.I still remember his words, "the Hamiltonian is the same anyway", which he said after agreeing my proposal.I also would like to thank him to allow me to the Leading Graduate Program in Science and Engineering and Power Energy Professional WISE Program.These programs require extra work for some unique curriculums, such as Lab.Rotations, internship and studying abroad.He has been supportive and flexible all the time and gave me full room to what I needed to do.All these works could not be done without support and guidance.Next, I would like to thank the members of Macroscopic Quantum Physics Project, National Institute of Information and Communication Technologies (NICT).I greatly appreciate Kouichi Semba, the leader of the project, letting me join the team and supported my PhD studies.He recommended me to Prof. William D. Oliver at MIT which made my visiting stay at EQuS at MIT become true.I also want to thank you him for applying for the fund by CREST which greatly helped me financially for a period of working at NICT.His advices and supports were not only very helpful for the works but also enriched my life.Fumiki Yoshihara was my mentor all the time during these works.He told me how to design and analyze the circuits, prepare the samples and operate the systems for experiments.He always answered me when I face problems and help me solve them, even they are easy ones.It has to be pointed out that he gave me the idea coupling the qubit to multiple modes in the resonator.This research topic has been tough due to its complicity, yet also been fun to mess around.I also appreciate he invited me to the soccer games during the lunch breaks.The cryostat which I used to cool the circuits was mostly prepared by Tomoko Fuse.She also told me how to prepare the cryostat and manage the cables inside it.Her advices and comments on my works were always greatly helpful.As a theorist Sahel Ashhab supported my works from the basic ideas.His advices helped me a lot to understand what is happening in the systems.He also helped me analyze the multimode circuit QED system by carefully deriving the expressions.I would like to thank the of the group, Sunmi Kim, with the discussions over chip designs and preparation of the Lab.At the end, I thank Akiko Hoshi for dealing all the paper works and Takashi Nakayama for helping me with the coding and equipment preparation.Thirdly, I would like to thank Shiro Saito and Kosuke Kakuyanagi from Superconducting Quantum Circuits Research Group at NTT Basic Research Laboratories.As the co-authors, they fabricated the samples with maximum care.I also appreciate the discussions about the experimental results where they always gave helpful advices and suggestions.I would like to thank all the members for the discussions during my iii internship at the same group.I especially thank Shiro Saito and Satoru Toida, the mentor during the internship, to let me join the group and conduct experiments.It was a great experience to work with the top-level researchers around the globe.I also would like to thank my two supervisors of the two Lab.Rotations, Kazuya Yuasa and Hiroshi Kawarada, for giving me the opportunity to join them.Although they were for a short period of time, the experiences broaden my interests towards science and engineering and will be surely valuable for me.I am deeply grateful to my supervisor of Engineering Quantum Systems group, William D. Oliver, for making me joining with he and the other Laboratory members and hosted my stay.I also appreciate the discussions and works with Roni Winik, who patiently explained his research and brought me in with his research topic.I spent a great time discussing and chatting with the group members and enjoyed working with them.I also want to thank William D. Oliver who applied a