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BCG) Is a Global Management Consulting Firm and the World’S Leading Advisor on Business Strategy
The Next Decade in Quantum Computing— and How to Play Boston Consulting Group (BCG) is a global management consulting firm and the world’s leading advisor on business strategy. We partner with clients from the private, public, and not-for-profit sectors in all regions to identify their highest-value opportunities, address their most critical challenges, and transform their enterprises. Our customized approach combines deep insight into the dynamics of companies and markets with close collaboration at all levels of the client organization. This ensures that our clients achieve sustainable competitive advantage, build more capable organizations, and secure lasting results. Founded in 1963, BCG is a private company with offices in more than 90 cities in 50 countries. For more information, please visit bcg.com. THE NEXT DECADE IN QUANTUM COMPUTING— AND HOW TO PLAY PHILIPP GERBERT FRANK RUESS November 2018 | Boston Consulting Group CONTENTS 3 INTRODUCTION 4 HOW QUANTUM COMPUTERS ARE DIFFERENT, AND WHY IT MATTERS 6 THE EMERGING QUANTUM COMPUTING ECOSYSTEM Tech Companies Applications and Users 10 INVESTMENTS, PUBLICATIONS, AND INTELLECTUAL PROPERTY 13 A BRIEF TOUR OF QUANTUM COMPUTING TECHNOLOGIES Criteria for Assessment Current Technologies Other Promising Technologies Odd Man Out 18 SIMPLIFYING THE QUANTUM ALGORITHM ZOO 21 HOW TO PLAY THE NEXT FIVE YEARS AND BEYOND Determining Timing and Engagement The Current State of Play 24 A POTENTIAL QUANTUM WINTER, AND THE OPPORTUNITY THEREIN 25 FOR FURTHER READING 26 NOTE TO THE READER 2 | The Next Decade in Quantum Computing—and How to Play INTRODUCTION he experts are convinced that in time they can build a Thigh-performance quantum computer. -
Quantum Magnonics with a Macroscopic Ferromagnetic Sphere
Quantum magnonics with a macroscopic ferromagnetic sphere Yasunobu Nakamura Superconducting Quantum Electronics Team Center for Emergent Matter Science (CEMS), RIKEN Research Center for Advanced Science and Technology (RCAST), The University of Tokyo Quantum Information Physics & Engineering Lab @ UTokyo http://www.qc.rcast.u-tokyo.ac.jp/ The magnonists Ryosuke Mori Seiichiro Ishino Dany Lachance-Quirion (Sherbrooke) Yutaka Tabuchi Alto Osada Koji Usami Ryusuke Hisatomi Quantum mechanics in macroscopic scale Quantum state control of collective excitation modes in solids Superconductivity Microscopic Surface Macroscopic plasmon Ordered phase Charge polariton Broken symmetry Photon Photon Spin Atom Magnon Phonon Ferromagnet Lattice order • Spatially-extended rigid mode • Large transition moment Superconducting qubit – nonlinear resonator LC resonator Josephson junction resonator Josephson junction = nonlinear inductor anharmonicity ⇒ effective two-level system energy inductive energy = confinement potential charging energy = kinetic energy ⇒ quantized states Quantum interface between microwave and light • Quantum repeater • Quantum computing network Hybrid quantum systems Superconducting quantum electronics Superconducting circuits Surface Nonlinearity plasmon polariton Quantum Quantum magnonics nanomechanics Microwave Ferromagnet Nanomechanics Magnon Phonon Light Quantum surface acoustics Quantum magnonics Hybrid with paramagnetic spin ensembles Spin ensemble of NV-centers in diamond Kubo et al. PRL 107, 220501 (2011). CEA Saclay Zhu et -
Chapter 3 Quantum Circuit Model of Computation
Chapter 3 Quantum Circuit Model of Computation 3.1 Introduction In the previous chapter we saw that any Boolean function can be computed from a reversible circuit. In particular, in principle at least, this can be done from a small set of universal logical gates which do not dissipate heat dissi- pation (so we have logical reversibility as well as physical reversibility. We also saw that quantum evolution of the states of a system (e.g. a collection of quantum bits) is unitary (ignoring the reading or measurement process of the bits). A unitary matrix is of course invertible, but also conserves entropy (at the present level you can think of this as a conservation of scalar prod- uct which implies conservation of probabilities and entropies). So quantum evolution is also both \logically" and physically reversible. The next natural question is then to ask if we can use quantum operations to perform computational tasks, such as computing a Boolean function? Do the principles of quantum mechanics bring in new limitations with respect to classical computations? Or do they on the contrary bring in new ressources and advantages? These issues were raised and discussed by Feynman, Benioff and Manin in the early 1980's. In principle QM does not bring any new limitations, but on the contrary the superposition principle applied to many particle systems (many qubits) enables us to perform parallel computations, thereby speed- ing up classical computations. This was recognized very early by Feynman who argued that classical computers cannot simulate efficiently quantum me- chanical processes. The basic reason is that general quantum states involve 1 2 CHAPTER 3. -
Optimization of Reversible Circuits Using Toffoli Decompositions with Negative Controls
S S symmetry Article Optimization of Reversible Circuits Using Toffoli Decompositions with Negative Controls Mariam Gado 1,2,* and Ahmed Younes 1,2,3 1 Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21568, Egypt; [email protected] 2 Academy of Scientific Research and Technology(ASRT), Cairo 11516, Egypt 3 School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK * Correspondence: [email protected]; Tel.: +203-39-21595; Fax: +203-39-11794 Abstract: The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. This paper proposes two methods to reduce the quantum cost of 3-bit reversible circuits. The first method utilizes basic building blocks of gate pairs using different Toffoli decompositions. These gate pairs are used to reconstruct the quantum circuits where further optimization rules will be applied to synthesize the optimized circuit. The second method suggests using a new universal library, which provides better quantum cost when compared with previous work in both cost015 and cost115 metrics; this proposed new universal library “Negative NCT” uses gates that operate on the target qubit only when the control qubit’s state is zero. A combination of the proposed basic building blocks of pairs of gates and the proposed Negative NCT library is used in this work for synthesis and optimization, where the Negative NCT library showed better quantum cost after optimization compared with the NCT library despite having the same circuit size. The reversible circuits over three bits form a permutation group of size 40,320 (23!), which Citation: Gado, M.; Younes, A. -
Multi-Mode Ultra-Strong Coupling in Circuit Quantum Electrodynamics
www.nature.com/npjqi ARTICLE OPEN Multi-mode ultra-strong coupling in circuit quantum electrodynamics Sal J. Bosman1, Mario F. Gely1, Vibhor Singh2, Alessandro Bruno3, Daniel Bothner1 and Gary A. Steele1 With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency ωa,m and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g/ωm = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling. npj Quantum Information (2017) 3:46 ; doi:10.1038/s41534-017-0046-y INTRODUCTION decreasing gate times20 as well as the performance of quantum 21 Superconducting circuits such as microwave cavities and Joseph- memories. With very strong coupling rates, the additional modes son junction based artificial atoms1 have opened up a wealth of of an electromagnetic resonator become increasingly relevant, new experimental possibilities by enabling much stronger light- and U/DSC can only be understood in these systems if the multi- matter coupling than in analog experiments with natural atoms2 mode effects are correctly modeled. -
Concentric Transmon Qubit Featuring Fast Tunability and an Anisotropic Magnetic Dipole Moment
Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment Cite as: Appl. Phys. Lett. 108, 032601 (2016); https://doi.org/10.1063/1.4940230 Submitted: 13 October 2015 . Accepted: 07 January 2016 . Published Online: 21 January 2016 Jochen Braumüller, Martin Sandberg, Michael R. Vissers, Andre Schneider, Steffen Schlör, Lukas Grünhaupt, Hannes Rotzinger, Michael Marthaler, Alexander Lukashenko, Amadeus Dieter, Alexey V. Ustinov, Martin Weides, and David P. Pappas ARTICLES YOU MAY BE INTERESTED IN A quantum engineer's guide to superconducting qubits Applied Physics Reviews 6, 021318 (2019); https://doi.org/10.1063/1.5089550 Planar superconducting resonators with internal quality factors above one million Applied Physics Letters 100, 113510 (2012); https://doi.org/10.1063/1.3693409 An argon ion beam milling process for native AlOx layers enabling coherent superconducting contacts Applied Physics Letters 111, 072601 (2017); https://doi.org/10.1063/1.4990491 Appl. Phys. Lett. 108, 032601 (2016); https://doi.org/10.1063/1.4940230 108, 032601 © 2016 AIP Publishing LLC. APPLIED PHYSICS LETTERS 108, 032601 (2016) Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment Jochen Braumuller,€ 1,a) Martin Sandberg,2 Michael R. Vissers,2 Andre Schneider,1 Steffen Schlor,€ 1 Lukas Grunhaupt,€ 1 Hannes Rotzinger,1 Michael Marthaler,3 Alexander Lukashenko,1 Amadeus Dieter,1 Alexey V. Ustinov,1,4 Martin Weides,1,5 and David P. Pappas2 1Physikalisches Institut, Karlsruhe Institute of Technology, -
Quantum Computational Complexity Theory Is to Un- Derstand the Implications of Quantum Physics to Computational Complexity Theory
Quantum Computational Complexity John Watrous Institute for Quantum Computing and School of Computer Science University of Waterloo, Waterloo, Ontario, Canada. Article outline I. Definition of the subject and its importance II. Introduction III. The quantum circuit model IV. Polynomial-time quantum computations V. Quantum proofs VI. Quantum interactive proof systems VII. Other selected notions in quantum complexity VIII. Future directions IX. References Glossary Quantum circuit. A quantum circuit is an acyclic network of quantum gates connected by wires: the gates represent quantum operations and the wires represent the qubits on which these operations are performed. The quantum circuit model is the most commonly studied model of quantum computation. Quantum complexity class. A quantum complexity class is a collection of computational problems that are solvable by a cho- sen quantum computational model that obeys certain resource constraints. For example, BQP is the quantum complexity class of all decision problems that can be solved in polynomial time by a arXiv:0804.3401v1 [quant-ph] 21 Apr 2008 quantum computer. Quantum proof. A quantum proof is a quantum state that plays the role of a witness or certificate to a quan- tum computer that runs a verification procedure. The quantum complexity class QMA is defined by this notion: it includes all decision problems whose yes-instances are efficiently verifiable by means of quantum proofs. Quantum interactive proof system. A quantum interactive proof system is an interaction between a verifier and one or more provers, involving the processing and exchange of quantum information, whereby the provers attempt to convince the verifier of the answer to some computational problem. -
General-Purpose Quantum Circuit Simulator with Projected Entangled-Pair States and the Quantum Supremacy Frontier
PHYSICAL REVIEW LETTERS 123, 190501 (2019) General-Purpose Quantum Circuit Simulator with Projected Entangled-Pair States and the Quantum Supremacy Frontier Chu Guo,1,* Yong Liu ,2,* Min Xiong,2 Shichuan Xue,2 Xiang Fu ,2 Anqi Huang,2 Xiaogang Qiang ,2 Ping Xu,2 Junhua Liu,3,4 Shenggen Zheng,5 He-Liang Huang,1,6,7 Mingtang Deng,2 † ‡ Dario Poletti,8, Wan-Su Bao,1,7, and Junjie Wu 2,§ 1Henan Key Laboratory of Quantum Information and Cryptography, IEU, Zhengzhou 450001, China 2Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology, Changsha 410073, China 3Information Systems Technology and Design, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore 4Quantum Intelligence Lab (QI-Lab), Supremacy Future Technologies (SFT), Guangzhou 511340, China 5Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China 6Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 7CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 8Science and Math Cluster and EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore (Received 30 July 2019; published 4 November 2019) Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Here, we bring together many-body quantum physics and quantum computing by using a method for strongly interacting two-dimensional systems, the projected entangled-pair states, to realize an effective general-purpose simulator of quantum algorithms. -
Topological Quantum Computation Zhenghan Wang
Topological Quantum Computation Zhenghan Wang Microsoft Research Station Q, CNSI Bldg Rm 2237, University of California, Santa Barbara, CA 93106-6105, U.S.A. E-mail address: [email protected] 2010 Mathematics Subject Classification. Primary 57-02, 18-02; Secondary 68-02, 81-02 Key words and phrases. Temperley-Lieb category, Jones polynomial, quantum circuit model, modular tensor category, topological quantum field theory, fractional quantum Hall effect, anyonic system, topological phases of matter To my parents, who gave me life. To my teachers, who changed my life. To my family and Station Q, where I belong. Contents Preface xi Acknowledgments xv Chapter 1. Temperley-Lieb-Jones Theories 1 1.1. Generic Temperley-Lieb-Jones algebroids 1 1.2. Jones algebroids 13 1.3. Yang-Lee theory 16 1.4. Unitarity 17 1.5. Ising and Fibonacci theory 19 1.6. Yamada and chromatic polynomials 22 1.7. Yang-Baxter equation 22 Chapter 2. Quantum Circuit Model 25 2.1. Quantum framework 26 2.2. Qubits 27 2.3. n-qubits and computing problems 29 2.4. Universal gate set 29 2.5. Quantum circuit model 31 2.6. Simulating quantum physics 32 Chapter 3. Approximation of the Jones Polynomial 35 3.1. Jones evaluation as a computing problem 35 3.2. FP#P-completeness of Jones evaluation 36 3.3. Quantum approximation 37 3.4. Distribution of Jones evaluations 39 Chapter 4. Ribbon Fusion Categories 41 4.1. Fusion rules and fusion categories 41 4.2. Graphical calculus of RFCs 44 4.3. Unitary fusion categories 48 4.4. Link and 3-manifold invariants 49 4.5. -
Interplay Between Kinetic Inductance, Nonlinearity, and Quasiparticle Dynamics in Granular Aluminum Microwave Kinetic Inductance Detectors
PHYSICAL REVIEW APPLIED 11, 054087 (2019) Interplay Between Kinetic Inductance, Nonlinearity, and Quasiparticle Dynamics in Granular Aluminum Microwave Kinetic Inductance Detectors Francesco Valenti,1,2 Fabio Henriques,1 Gianluigi Catelani,3 Nataliya Maleeva,1 Lukas Grünhaupt,1 Uwe von Lüpke,1 Sebastian T. Skacel,4 Patrick Winkel,1 Alexander Bilmes,1 Alexey V. Ustinov,1,5 Johannes Goupy,6 Martino Calvo,6 Alain Benoît,6 Florence Levy-Bertrand,6 Alessandro Monfardini,6 and Ioan M. Pop1,4,* 1 Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany 2 Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany 3 JARA Institute for Quantum Information (PGI-11), Forschungszentrum Jülich, 52425 Jülich, Germany 4 Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany 5 Russian Quantum Center, National University of Science and Technology MISIS, 119049 Moscow, Russia 6 Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France (Received 9 November 2018; revised manuscript received 8 March 2019; published 31 May 2019) Microwave kinetic inductance detectors (MKIDs) are thin-film, cryogenic, superconducting resonators. Incident Cooper pair-breaking radiation increases their kinetic inductance, thereby measurably lower- ing their resonant frequency. For a given resonant frequency, the highest MKID responsivity is obtained by maximizing the kinetic inductance fraction α. However, in circuits with α close to unity, the low supercurrent density reduces the maximum number of readout photons before bifurcation due to self-Kerr nonlinearity, therefore setting a bound for the maximum α before the noise-equivalent power (NEP) starts to increase. By fabricating granular aluminum MKIDs with different resistivities, we effectively sweep their kinetic inductance√ from tens to several hundreds of pH per square. -
Lecture 1: Introduction to the Quantum Circuit Model September 9, 2015 Lecturer: Ryan O’Donnell Scribe: Ryan O’Donnell
Quantum Computation (CMU 18-859BB, Fall 2015) Lecture 1: Introduction to the Quantum Circuit Model September 9, 2015 Lecturer: Ryan O'Donnell Scribe: Ryan O'Donnell 1 Overview of what is to come 1.1 An incredibly brief history of quantum computation The idea of quantum computation was pioneered in the 1980s mainly by Feynman [Fey82, Fey86] and Deutsch [Deu85, Deu89], with Albert [Alb83] independently introducing quantum automata and with Benioff [Ben80] analyzing the link between quantum mechanics and reversible classical computation. The initial idea of Feynman was the following: Although it is perfectly possible to use a (normal) computer to simulate the behavior of n-particle systems evolving according to the laws of quantum, it seems be extremely inefficient. In particular, it seems to take an amount of time/space that is exponential in n. This is peculiar because the actual particles can be viewed as simulating themselves efficiently. So why not call the particles themselves a \computer"? After all, although we have sophisticated theoretical models of (normal) computation, in the end computers are ultimately physical objects operating according to the laws of physics. If we simply regard the particles following their natural quantum-mechanical behavior as a computer, then this \quantum computer" appears to be performing a certain computation (namely, simulating a quantum system) exponentially more efficiently than we know how to perform it with a normal, \classical" computer. Perhaps we can carefully engineer multi-particle systems in such a way that their natural quantum behavior will do other interesting computations exponentially more efficiently than classical computers can. -
Synthesis of Topological Quantum Circuits
Synthesis of Topological Quantum Circuits Alexandru Paler1 Simon Devitt2 Kae Nemoto2 Ilia Polian1 1Faculty of Informatics and Mathematics 2National Institute of Informatics University of Passau 2-1-2 Hitotsubashi, Chiyoda-ku Innstr. 43, D-94032 Passau, Germany Tokyo, Japan [email protected] [email protected] Abstract—Topological quantum computing has recently proven converting the abstract circuits describing a quantum algorithm itself to be a very powerful model when considering large- into the full set of error corrected operations applied by scale, fully error corrected quantum architectures. In addition the actual hardware. This work represents arguably the first to its robust nature under hardware errors, it is a software driven method of error corrected computation, with the hardware serious attempt to develop a classical framework for a fully responsible for only creating a generic quantum resource (the error corrected computational model compatible with current topological lattice). Computation in this scheme is achieved by architectural designs. the geometric manipulation of holes (defects) within the lattice. Interactions between logical qubits (quantum gate operations) Topological Quantum Computing (TQC) is a model for are implemented by using particular arrangements of the defects, universal computation that is constructed on the framework such as braids and junctions. We demonstrate that junction-based of active error correction. This method of computation very topological quantum gates allow highly regular and structured abstract when compared to classical computer science. One implementation of large CNOT (controlled-not) gate networks, of the more bizarre aspects of this model is that the physi- which ultimately form the basis of the error corrected primitives that must be used for an error corrected algorithm.