Engineering the coupling of superconducting qubits Von der Fakultät für Mathematik, Informatik und Naturwissenschaften der RWTH Aachen University zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von M. Sc. Alessandro Ciani aus Penne, Italien Berichter: Prof. Dr. David DiVincenzo Prof. Dr. Fabian Hassler Tag der mündlichen Prüfung: 12 April 2019 Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek verfügbar. ii «Considerate la vostra semenza: fatti non foste a viver come bruti, ma per seguir virtute e conoscenza.» Dante Alighieri, "La Divina Commedia", Inferno, Canto XXVI, vv. 118-120. iii Abstract The way to build a scalable and reliable quantum computer that truly exploits the quantum power faces several challenges. Among the various proposals for building a quantum computer, superconducting qubits have rapidly progressed and hold good promises in the near-term future. In particular, the possibility to design the required interactions is one of the most appealing features of this kind of architecture. This thesis deals with some detailed aspects of this problem focusing on architectures based on superconducting transmon-like qubits. After reviewing the basic tools needed for the study of superconducting circuits and the main kinds of superconducting qubits, we move to the analyisis of a possible scheme for realizing direct parity measurement. Parity measurements, or in general stabilizer measurements, are fundamental tools for realizing quantum error correct- ing codes, that are believed to be fundamental for dealing with the problem of de- coherence that affects any physical implementation of a quantum computer. While these measurements are usually done indirectly with the help of ancilla qubits, the scheme that we analyze performs the measurement directly, and requires the engi- neering of a precise matching condition. We show how sufficient freedom in the design of the interactions can be achieved with tunable coupling qubits, which are a variant of transmon qubits. In the second part of the thesis, we study instead an alternative model for quan- tum computation and a possible realization with transmon qubits. The model per- forms a quantum computation with a time-independent Hamiltonian and it is closely connected to one of the original proposals for a quantum computer due to Feynman. After explaining the basic ideas of the model, we also discuss a new version with a modified dynamics compared to previous proposals, which maps exactly to Feyn- man’s original idea, and also how to realize a Toffoli gate in the model. We then move to the analysis of an implementation with transmon qubits. We show how it is possible to engineer the Hamiltonian that performs the desired computation in a completely passive way, and with the desired range of parameters, limiting spuri- ous, unwanted terms. Zusammenfassung Die Realisierung eines skalierbaren und zuverlässigen Quantencomputers, der tat- sächlich die Quanten-Vorteile ausnutzt, steht vor mehreren Herausforderungen. Un- ter den verschiedenen Vorschlägen einer Implementierung eines Quantencomputers haben sich supraleitende Qubits rasch verbessert und sind sehr vielversprechend in absehbarer Zukunft. Insbesondere die Möglichkeit, die benötigten Wechselwirkun- gen einzustellen, ist eine der attraktivsten Eigenschaften dieser Architektur. Diese Dissertation handelt von einigen detaillierten Aspekten dieses Problems, wobei Ar- chitekturen, welche auf supraleitende Qubits ähnlich dem Transmon basieren, im Vordergrund stehen. Nach der Besprechung grundlegender Werkzeuge, die für die Untersuchung supraleitender Schaltkreise benötigt werden, sowie der wichtigsten supraleitenden Qubits analysieren wir einen möglichen Entwurf für die Realisierung einer direkten Paritätsmessung. Die Messungen der Parität, bzw. i.A. sogenannte „stabilizer“ Mes- sungen, sind fundamentale Werkzeuge für die Realisierung einer Quantenfehlerkor- rektur. Diese ist fundamental, um das Problem der Dekohärenz, die jede physikali- sche Implementierung eines Quantencomputers beeinflusst, zu umgehen. Während diese Messungen normalerweise indirekt mit Hilfs-Qubits ausgeführt werden, ana- lysieren wir ein Schema, das diese Messungen direkt ausführt, jedoch die Anpas- sung einer genauen Bedingung voraussetzt. Wir zeigen, wie ausreichend Freiheiten in der Gestaltung der Wechselwirkung mit „tunable coupling qubits“, die eine Vari- ante des Transmons sind, erreicht werden können. Im zweiten Teil dieser Dissertation betrachten wir ein alternatives Modell eines Quantencomputers sowie eine mögliche Realisierung mit Transmons. Dieses Modell realisiert einen Quantencomputer mit einem zeitunabhängigen Hamilton-Operator und ist nah verwandt mit dem ursprünglichen Modell eines Quantencomputers, das von Feynman vorgeschlagen wurde. Nach der Einführung der Grundideen dieses Modells analysieren wir eine neue Version mit modifizierter Dynamik, welche exakt mit Feynmans ursprünglicher Idee übereinstimmt. Außerdem wird gezeigt, wie das Toffoli-Gatter in diesem Modell realisiert wird. Im Anschluss folgt eine Analyse der Implementierung mit Transmons. Wir zeigen, wie es möglich ist einen Hamilton- Operator zu konstruieren, der die gewünschte Rechnung in einer komplett passiven Arten und Weise sowie mit der gewünschten Bandbreite der Parameter ausführt, wobei störende, unerwünschte Terme limitiert werden. vii Acknowledgements During these years I’ve always thought about the moment in which I would have written the acknowledgements of my thesis, and finally on a Sunday morning here I am. I would like to begin by thanking my supervisor David DiVincenzo, who almost four years ago believed in a crazy italian engineer who wanted to move to quantum physics. Thank you for guiding me during these years and patiently teaching me how to be a physicist through all the daily difficulties. I deeply admire your passion and curiosity towards discovering new things, and I hope that this passion will also always be with me for the rest of my life. I also thank Barbara Terhal for giving me the opportunity to work with her and for the contagious entuhsiasm that she puts in her job. I really enjoyed working with you and I thank you for all I learned, and I continue to learn from you, and I mean not only about phyiscs. My thanks go also to Fabian Hassler who taught me the importance of devel- oping a physical intuition in any problem we treat. Thanks also for reviewing this thesis and for always being available for discussions when I was randomly stepping into your office. I deeply thank all my friends of the IQI that I met in these years. First of all, I would like to thank my legendary office mate Stefano Bosco, with whom I shared the office for almost all the period of my PhD. I loved our fights about physics, in particular about Bloch’s theorem in presence of magnetic field, and I will miss our daily office life. Also thank you for fostering my knowledge of italian trash music. I also thank my first office mate Firat Solgun for welcoming me when I arrived here. I never told you that the first night we went out together I really disliked the turkish food we had, and it is finally time for the truth. I would also like to thank all the people who shared the office with me even only for a brief period: Jonathan Conrad (also for helping me with my exam), Joris Dolderer, Sander Konijnenberg, Fatemeh Hajiloo, Eva Fluck and Rijul Sachdeva. Thank you Manuel Rispler and Susanne Richer for being my patient german teachers during these years. I thank Manuel also for helping me through the crazy paperwork of german burocracy, and Susanne for always reminding me how good I am in quitting smoking. I thank also Cica Gustiani for the "amazing" indonesian cigarettes she brought back for me from Indonesia. I thank Nikolas Breuckmann for always sharing provoking pictures of weird pizzas with me. I thank Ben Criger for explaining to me many things about the canadian culture, and in particular who Wayne Gretzki is. I thank also Ben and Jakob Stubenrauch for our works together. Special thanks go also to Martin Rymarz who helped me translating the abstract of this thesis, and for all the help he provided in the last period. I deeply appreciate the fact that you are believing in the "liketattico" project and developing the app in this very moment. viii I continue by thanking Daniel Otten for giving me the opportunity to become the legendary "spanish guy" of quantum optics, and for sharing with me this last period of thesis submission. I also thank Federica Haupt, in particular for giving to me as a present a mixer , that exploded in my hands few days ago, and for really nice dinners, and also Ananda Roy for listening to me when I said that the Guns n’ Roses are (by far) the best band of all times, and for explaining to us the correct and non-trivial pronounciation of his name (no, it is not Amanda!). I thank Fabio Pedrocchi for all the time we spent at the gym together without results. I thank Benedikt Placke for teaching me that golf is indeed a sport, and Lucia Gonzalez Rosado, for telling me that it is possible to survive one year of erasmus cooking only with the microwave oven. I thank Alexander Ziesen for still believing in the fact that one day I will come back to play football with the IQI. My special thanks go also to Lisa Arndt for her always positive mood, and Uta Meyer, for her resilience to the above-mentioned italian trash music. I also spent a really nice time with Jascha Ulrich and Amin Hosseinkhani at the conference of the condensed matter division of the European Physical society in Groningen, and with Roman Riwar and Kenneth Goodenough at the APS meeting in New Orleans, and I thank you for those nice moments. I am also grateful to Gianluigi Catelani for inviting me to the conference in Groningen and to Shabir Barzanjeh for the invitation to the conference "Frontiers in circuit QED" in Vienna. I would also like to thank Andrew Goldsborough for his extremely accurate political predictions of the last years. I thank Maarten Wegewjis for all the times I stole coffee from him, and Norbert Schuch for the answers he gave me on http://physics.stackexchange.com.