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In Situ Quantum Control Over Superconducting Qubits ! In situ quantum control over superconducting qubits Anatoly Kulikov M.Sc. A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2020 School of Mathematics and Physics ARC Centre of Excellence for Engineered Quantum Systems (EQuS) ABSTRACT In the last decade, quantum information processing has transformed from a field of mostly academic research to an applied engineering subfield with many commercial companies an- nouncing strategies to achieve quantum advantage and construct a useful universal quantum computer. Continuing efforts to improve qubit lifetime, control techniques, materials and fab- rication methods together with exploring ways to scale up the architecture have culminated in the recent achievement of quantum supremacy using a programmable superconducting proces- sor { a major milestone in quantum computing en route to useful devices. Marking the point when for the first time a quantum processor can outperform the best classical supercomputer, it heralds a new era in computer science, technology and information processing. One of the key developments enabling this transition to happen is the ability to exert more precise control over quantum bits and the ability to detect and mitigate control errors and imperfections. In this thesis, ways to efficiently control superconducting qubits are explored from the experimental viewpoint. We introduce a state-of-the-art experimental machinery enabling one to perform one- and two-qubit gates focusing on the technical aspect and outlining some guidelines for its efficient operation. We describe the software stack from the time alignment of control pulses and triggers to the data processing organisation. We then bring in the standard qubit manipulation and readout methods and proceed to describe some of the more advanced optimal control and calibration techniques. The described toolbox together with some newly developed advances such as multi-level single-shot readout are applied to a practical problem of generating high-quality random num- bers. Following the recent advances in the field, we certify our generator based on the Kochen- Specker theorem utilizing contextuality of quantum mechanics as an underlying resource of randomness. Our implementation based on the solid-state circuit quantum electrodynamics (QED) platform and the new certification scheme allows us to greatly enhance the bit rate of certified quantum random number generators (QRNGs) and approach the requirements for real-world applications. Addressing some of the control and state preparation errors, we develop a set of techniques to use a qubit as an in situ probe of distortions of its control lines and its effective temperature. Considering a qubit simultaneously driven by a longitudinal and a transverse MW-drives under certain resonant conditions, we show that in the rotating dressed-state picture (second rotating frame) one can get information about both the amplitude and the phase of the drive signals. This allows us to employ a qubit as an on-chip vector network analyzer and precisely measure the transfer functions of its control lines. As no other method with comparable frequency domain coverage exists, we verify our technique by cancelling out the distortions and increasing the i fidelity of entangling two-qubit CPHASE gate. Finally, we show that the decay of the correlations between two sequential measurements of a quantum bit is a manifestation of its nonzero effective temperature. We use it to develop a precise method of evaluating the qubits population allowing for virtually unlimited suppression of absolute errors. We realize the method and demonstrate its applicability to the calibration of a quantum processor and evaluation of active reset techniques. As the actual mechanism of the increased excited-state population is currently unknown, we use our method's precision to show the qubit's coupling to two separate independent thermal baths. We also introduce the `temperature spectroscopy' as a tool to acquire more information about the qubits spurious excitation sources. ii DECLARATION BY AUTHOR This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including devel- opment of concepts, data analysis and post-processing, experimental techniques, professional editorial advice, and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my research higher degree candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis. iii PUBLICATIONS DURING CANDIDATURE Peer-reviewed publications 1. Measuring effective temperatures of qubits using correlations, A. Kulikov, R. Navarathna, and A. Fedorov Phys. Rev. Lett. 124 240501 (2020) 2. In situ Characterization of Qubit Control Lines: A Qubit as a Vector Network Analyzer, M. Jerger, A. Kulikov, Z. Vasselin, and A. Fedorov Phys. Rev. Lett. 123, 150501 (2019) 3. On the chromatic number of small-dimensional Euclidean spaces, D. Cherkashin, A. Kulikov, and A. Raigorodskii Discrete Applied Mathematics 243, 125-131 (2018) 4. Realization of a Quantum Random Number Generator Certified with the Kochen-Specker Theorem, A. Kulikov, M. Jerger, A. Potoˇcnik,A. Wallraff, and A. Fedorov Phys. Rev. Lett. 119, 240501 (2017) iv PUBLICATIONS INCLUDED IN THIS THESIS Realization of a Quantum Random Number Generator Certified with the Kochen-Specker Theorem, A. Kulikov, M. Jerger, A. Potoˇcnik, A. Wallraff, and A. Fedorov Phys. Rev. Lett. 119, 240501 (2017). (Included in Chapter4.) Contributor Statement of contribution A. Kulikov Planning the experiment (Candidate) Conducting the measurements Analysis of the data Writing the manuscript Referee replies and final manuscript revision M. Jerger Building the measurement setup Assisting with the measurements Co-supervising the project A. Potoˇcnik Fabricating the parametric amplifier A. Wallraff A. Fedorov Supervising the project Fabricating the qubit Writing the manuscript In situ Characterization of Qubit Control Lines: A Qubit as a Vector Network Analyzer, M. Jerger, A. Kulikov, Z. Vasselin, and A. Fedorov Phys. Rev. Lett. 123, 150501 (2019). (Included in Chapter5.) v Contributor Statement of contribution A. Kulikov Developing the software (Candidate) Conducting the measurements (gate optimisation) Analysis of the data (gate optimisation) Writing the final manuscript Referee replies and final manuscript revision M. Jerger Developing the theoretical proposal Planning the experiment Developing the software Conducting the measurements (line calibration) Analysis of the data (line calibration) Writing the initial manuscript Z. Vasselin Performing the initial line calibration measurements A. Fedorov Supervising the project Fabricating the qubit Developing the theoretical protocol Writing the final manuscript Referee replies and final manuscript revision Measuring effective temperatures of qubits using correlations, A. Kulikov, R. Navarathna, and A. Fedorov Phys. Rev. Lett. 124 240501 (2020). (Included in Chapter6.) Contributor Statement of contribution A. Kulikov Planning the experiment (Candidate) Conducting the measurements Analysis of the data Writing the manuscript Referee replies and final manuscript revision R. Navarathna Conducting the measurements Analysis of the data Writing the manuscript Referee replies and final manuscript revision A. Fedorov Supervising the project Writing the manuscript Referee replies and final manuscript revision vi CONTRIBUTIONS BY OTHERS TO THE THESIS No contributions by others except as co-authors as outlined in the \Publications included in this thesis" section. vii STATEMENT OF PARTS OF THE THESIS SUBMITTED TO QUALIFY FOR THE AWARD OF ANOTHER DEGREE No work submitted towards another degree have been included in this thesis. viii RESEARCH INVOLVING HUMAN OR ANIMAL SUBJECTS No animal or human subjects were involved in this research. ix ACKNOWLEDGEMENTS First and foremost, I would like to thank my principal advisor Arkady Fedorov for introducing me to the exciting field of quantum technology, and for the invitation to pursue this PhD project in the SQD Lab in Australia. Your calm and focused work attitude together with clear understanding of theoretical and experimental concepts have taught me a great deal. Further, a perfect combination of guidance and freedom, and being always welcome to discuss ideas have made working with you very productive and enjoyable. The technical part of this work
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