Status of quantum computer development Entwicklungsstand Quantencomputer Document history Version Date Editor Description 1.0 May 2018 Document status after main phase of project 1.1 July 2019 First update containing both new material and improved readability, details summarized in chapters 1.6 and 2.11 1.2 June 2020 Second update containing new algorithmic developments, details summarized in chapters 1.6.2 and 2.12 Federal Office for Information Security Post Box 20 03 63 D-53133 Bonn Phone: +49 22899 9582-0 E-Mail: [email protected] Internet: https://www.bsi.bund.de © Federal Office for Information Security 2020 Introduction Introduction This study discusses the current (Fall 2017, update early 2019, second update early 2020 ) state of affairs in the physical implementation of quantum computing as well as algorithms to be run on them, focused on applications in cryptanalysis. It is supposed to be an orientation to scientists with a connection to one of the fields involved—mathematicians, computer scientists. These will find the treatment of their own field slightly superficial but benefit from the discussion in the other sections. The executive summary as well as the introduction and conclusions to each chapter provide actionable information to decision makers. The text is separated into multiple parts that are related (but not identical) to previous work packages of this project. Authors Frank K. Wilhelm, Saarland University Rainer Steinwandt, Florida Atlantic University, USA Brandon Langenberg, Florida Atlantic University, USA Per J. Liebermann, Saarland University Anette Messinger, Saarland University Peter K. Schuhmacher, Saarland University Aditi Misra-Spieldenner, Saarland University Copyright The study including all its parts are copyrighted by the BSI–Federal Office for Information Security. Any use outside the limits defined by the copyright law without approval by the BSI is not permitted and punishable. This covers reproduction, translation, micro filming, and storing and processing in electronic systems. BSI-Reference BSI Title: Entwicklungsstand Quantencomputer BSI Project Number: 283 Federal Office for Information Security 3 Table of Contents Table of Contents Document history.............................................................................................................................................................................. 2 Introduction......................................................................................................................................................................................... 3 Authors............................................................................................................................................................................................. 3 Copyright......................................................................................................................................................................................... 3 BSI-Reference................................................................................................................................................................................ 3 Index of Figures................................................................................................................................................................................... 9 Index of Tables.................................................................................................................................................................................. 13 1 Deutsche Zusammenfassung..................................................................................................................................................... 15 1.1 Was ist ein Quantencomputer?.......................................................................................................................................... 15 1.2 Die Relevanz von Quantencomputern für die Kryptoanalyse............................................................................15 1.3 Hardware für Quantencomputer......................................................................................................................................16 1.4 Aktuelle Entwicklungen........................................................................................................................................................ 19 1.5 Extrapolation.............................................................................................................................................................................. 19 1.6 Aktualisierungen....................................................................................................................................................................... 20 2 Synopsis................................................................................................................................................................................................ 23 2.1 Basic idea....................................................................................................................................................................................... 23 2.2 Hardware platforms................................................................................................................................................................. 23 2.3 Algorithmic goals...................................................................................................................................................................... 24 2.4 Computational Models........................................................................................................................................................... 24 2.5 Evaluation along computational models.......................................................................................................................26 2.6 Evaluation of platforms......................................................................................................................................................... 27 2.7 Extrapolation.............................................................................................................................................................................. 31 2.8 Alternative platforms.............................................................................................................................................................. 33 2.9 Global activities and potential for development........................................................................................................33 2.10 Risks................................................................................................................................................................................................. 33 2.11 Update Spring 2019.................................................................................................................................................................. 34 2.12 Update Spring 2020.................................................................................................................................................................. 34 Part I: Evaluating and benchmarking quantum computing hardware.................................................................36 3 Introduction to computational models and their requirements..............................................................................37 3.1 Structure and requirements of an evaluation system.............................................................................................37 3.2 Basic principles and notions of evaluating fault tolerant gate-based quantum computing.................38 4 Are recent quantum supremacy proposals relevant for cryptanalysis?................................................................41 4.1 Fault tolerance vs. near-term quantum supremacy.................................................................................................41 4.2 Algorithmic perspective......................................................................................................................................................... 41 5 Low-level analysis of qubit systems........................................................................................................................................ 44 5.1 Initial remarks............................................................................................................................................................................ 44 5.2 The DiVincenzo criteria reviewed..................................................................................................................................... 44 5.3 Coherence time scales............................................................................................................................................................. 46 5.4 Qubit definition indicators................................................................................................................................................... 49 Federal Office for Information Security 5 Table of Contents 5.5 Qubit initialization indicators............................................................................................................................................. 50 5.6 Readout indicators.................................................................................................................................................................... 50