DOCSLIB.ORG

Synthesis of Topological Quantum Circuits

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. We present cal hardware doesn’t actually perform any real computation. a number of heuristics to optimise the area of the resulting Instead, the hardware is only responsible for producing a structures and therefore the number of the required hardware very large three-dimensional lattice of qubits which are all resources. linked together to form a single, massive quantum state. This quantum state forms the workbench of the computation and I. INTRODUCTION information is created, processed and read-out via the strategic Quantum information science has been one of the extraor- manipulation of this massive quantum state produced from the dinary success stories of theoretical and experimental physics hardware [12]. The volume of this lattice directly relates to the in the last 20 years. Since the introduction of the field in the physical resources required for an error corrected algorithm. 1980s, there has been development of a complete theoretical As large quantum algorithms commonly require thousands of framework for universal quantum computation and repeated encoded qubits and high levels of error correction are often experimental demonstration of quantum control on a small needed, the volume of the lattice is an important criteria for the number of quantum bits (qubits) in multiple physical systems synthesis of large quantum circuits. Minimising this volume [1]. In addition to the experimental system development, there reduces the amount of physical resources required, and lowers have been multiple quantum architectures proposed demon- the costs of computation [13]. strating how a large-scale multi-million qubit machine could be constructed [2]–[7]. In the topological model, quantum gates are realised via Even with this level of experimental development, large geometric shapes, known as defects, moving through the scale quantum information processing requires hardware that lattice (e.g. see Fig. 2). These realisations enable highly regular arrangements which are easily optimised using discrete arXiv:1302.5182v1 [quant-ph] 21 Feb 2013 is extraordinarily accurate; many orders of magnitude higher than any system has ever demonstrated. The inherent inaccu- algorithms. Unlike in [11] where error corrected gates are racies in quantum hardware induces errors during processing realised by moving defects around each other (known as braid- which much be corrected via dedicated and resource intensive ing), we utilise a technique where gates are realised through Quantum Error Correcting (QEC) codes [8]. The topological junctions (where defects are jointed together in the lattice). model of QEC [9]–[11] has shown itself to be more promising These constructions of error corrected gates are minimal with to many other long-standing techniques and currently forms regard to the occupied lattice volume, and enable an efficient the basis of effectively all modern quantum-computing ar- placement within it. chitectures [4]–[7]. The continuing success of experimental This work presents compact representations for the neces- fabrication now requires us to seriously address the program- sary TQC quantum gates, and uses these for several heuristics ming and operation of a large scale computer. This work is that minimise the size of the required qubit lattice, known aimed at developing the required synthesis tools for large scale as the topological cluster. To the best of our knowledge, this quantum information processing in the context of a fully error is the first automatic quantum synthesis procedure with fully corrected system. We will present the classical framework for error corrected, TQC as the target technology. Lattice Provides a protective ”buffer” for QEC II. BACKGROUND A. Quantum Computing Quantum computing can be, to a certain extent, described by building parallels to classical computing. A comprehensive Unit Cell in of the lattice review of quantum information and computation can be found in [14]. The concept of classical bit has its quantum counter- part, called a quantum bit (qubit). Like in classical computing, quantum gates are used to manipulate the state of a qubit, but in contrast to classical gates, quantum gates always have an equal number of input and output qubits. The state of a qubit can be represented as a vector Defect: Encoded Qubit j i = α0j0i + α1j1i, where α0 and α1 are complex numbers (called amplitudes) that satisfy jα j2 + jα j2 = 1. Similarly to 0 1 Fig. 1. Logical volume of the topological cluster. Each red dot represents the classical world, j0i and j1i are the states that are analogue a physical qubit, green lines represent links (entanglement between qubits). to the classical bits 0 and 1. But unlike in classical computing, An encoded piece of information is a rectangular hole that is created by a qubit can be in a superposition of these two states, where it physically removing qubits internal to its boundary, the lattice surrounding the defect provides the error correction ”buffer”. The insert illustrates a unit is both 0 and 1. For example, the state α0j0i + α1j1i has cell of the lattice, consisting of 18 qubits. 2 a probability of jα0j of being measured in the j0i state 2 and a probability of jα1j of being measured in the j1i state. These states represent quantum wavefunctions and it Reading the value of a bit has a quantum counterpart; is the interference of these wavefunctions driving quantum measurement. Unlike classical readout, quantum measurement processing. Algorithms are designed such that the amplitude allows us to read out qubits in multiple ways. The standard related to the correct answer is amplified while the wrong measurement in quantum computation, referred to as a Z-basis answers are suppressed. measurement, measures if the qubit is in the j0i or j1i state, Another similarity between quantum computing and clas- collapsing (where the wavefunction describing the quantum sical computing is that computations can be expressed as state discontinuously changes) any superposition inconsistent circuits. Quantum circuits are a description of a quantum with the measurement result. Another type of measurement is algorithm (e.g. see Fig. 3). Quantum circuits have the input an X-basis measurement, which measures if the qubit is in on the left and the output on the right. The horizontal wires the p1 j i j i state or the p1 j i − j i state. This type 2 ( 0 + 1 ) 2 ( 0 1 ) represent the qubits, and the computation is performed by of measurement is valid as these two states are orthogonal applying a time ordered set of gates, left to right. (the wavefunctions describing these states have zero overlap). A quantum gate manipulating m qubits is described by In Fig. 3, the encircled X and Z are representing these two a 2m × 2m unitary matrix acting on an column vector of types of measurements. m length 2m with entries fα g where P2 −1 jα j2 = 1 for i i=0 i B. Topological Quantum Computing i 2 [0; ::; 2m − 1] representing the m-qubit state jφi = Pm−1 Several quantum architectures are based upon the model i=0 αijii. For example, the controlled-not gate (CNOT) acting on two qubits is defined by the following 4 × 4 matrix: of TQC [4]–[6], as this method for computation has QEC 0 1 integrated by construction. TQC is the preferred method for 1 0 0 0 three primary reasons. 1) It has one of the highest fault-tolerant B 0 1 0 0 C 2 CNOT = B C : (1) thresholds of any method of QEC . 2) It is a local model of @ 0 0 0 1 A computation, i.e. individual physical qubits in the computer 0 0 1 0 only have to interact with their neighbours. 3) The quantum Performing the CNOT operation between two qubits c and hardware is only used to prepare a large three-dimensional lat- t in some arbitrary quantum state1 results in the following tice of connected qubits (the topological cluster), algorithmic output: implementation is a function of how the lattice is consumed rather than how it is created. Therefore the TQC model is a jctiin = α00j00i + α01j01i + α10j10i + α11j11i software driven method of computation. jctiout = α00j00i + α01j01i + α10j11i + α11j10i (2) The specifics of how TQC works is complicated, however the general principal can be explained.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Luigi Frunzio
    THESE DE DOCTORAT DE L’UNIVERSITE PARIS-SUD XI spécialité: Physique des solides présentée par: Luigi Frunzio pour obtenir le grade de DOCTEUR de l’UNIVERSITE PARIS-SUD XI Sujet de la thèse: Conception et fabrication de circuits supraconducteurs pour l'amplification et le traitement de signaux quantiques soutenue le 18 mai 2006, devant le jury composé de MM.: Michel Devoret Daniel Esteve, President Marc Gabay Robert Schoelkopf Rapporteurs scientifiques MM.: Antonio Barone Carlo Cosmelli ii Table of content List of Figures vii List of Symbols ix Acknowledgements xvii 1. Outline of this work 1 2. Motivation: two breakthroughs of quantum physics 5 2.1. Quantum computation is possible 5 2.1.1. Classical information 6 2.1.2. Quantum information unit: the qubit 7 2.1.3. Two new properties of qubits 8 2.1.4. Unique property of quantum information 10 2.1.5. Quantum algorithms 10 2.1.6. Quantum gates 11 2.1.7. Basic requirements for a quantum computer 12 2.1.8. Qubit decoherence 15 2.1.9. Quantum error correction codes 16 2.2. Macroscopic quantum mechanics: a quantum theory of electrical circuits 17 2.2.1. A natural test bed: superconducting electronics 18 2.2.2. Operational criteria for quantum circuits 19 iii 2.2.3. Quantum harmonic LC oscillator 19 2.2.4. Limits of circuits with lumped elements: need for transmission line resonators 22 2.2.5. Hamiltonian of a classical electrical circuit 24 2.2.6. Quantum description of an electric circuit 27 2.2.7. Caldeira-Leggett model for dissipative elements 27 2.2.8.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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,
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Chapter 2 Quantum Gates
    Chapter 2 Quantum Gates “When we get to the very, very small world—say circuits of seven atoms—we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics. So, as we go down and fiddle around with the atoms down there, we are working with different laws, and we can expect to do different things. We can manufacture in different ways. We can use, not just circuits, but some system involving the quantized energy levels, or the interactions of quantized spins.” – Richard P. Feynman1 Currently, the circuit model of a computer is the most useful abstraction of the computing process and is widely used in the computer industry in the design and construction of practical computing hardware. In the circuit model, computer scien- tists regard any computation as being equivalent to the action of a circuit built out of a handful of different types of Boolean logic gates acting on some binary (i.e., bit string) input. Each logic gate transforms its input bits into one or more output bits in some deterministic fashion according to the definition of the gate. By compos- ing the gates in a graph such that the outputs from earlier gates feed into the inputs of later gates, computer scientists can prove that any feasible computation can be performed. In this chapter we will look at the types of logic gates used within circuits and how the notions of logic gates need to be modified in the quantum context.
    [Show full text]
  • Quantum Nonlinearities in Strong Coupling Circuit
    Q u a n t Circuit QED offers the possibility to realize an exceptionally strong coupling u between artificial atoms – individual superconducting qubits – and single m microwave photons in a one dimensional waveguide resonator. This new N o solid state approach to investigate the matter-light interaction on the level n l of individual quanta also represents a promising hardware architecture for i n the realization of a scalable quantum information processor. We first e a summarize and review the important theoretical and experimental r i principles of this rapidely developing field and give an overview of the t i e relevant literature. Here the focus is to provide a detailed discussion of the s i experimental ultra-low temperature measurement setup and the design, n fabrication and characterization of superconducting Josephson junction C i devices. Presented key experimental results include: 1) The first clear r c observation of the Jaynes-Cummings nonlinearity in the vacuum Rabi u i spectrum by measuring both two- and three-photon dressed states. 2) The t observation of strong collective coupling for up to 3 qubits. 3) A Q E quantitative investigation of the quantum to classical transition induced by D an elevated temperature environment. Johannes M. Fink Johannes M. Fink Quantum Nonlinearities in The author is a post doctoral scientist at the Swiss Strong Coupling Circuit QED Federal Institute of Technology Zurich. He studied in Vienna, Sydney and at ETH Zurich where he earned a On-Chip Quantum Optics with Microwave Photons Ph.D. in physics. His research is focused on designing, fabricating and controlling coherent devices for and Superconducting Electronic Circuits quantum optics and quantum information processing applications.
    [Show full text]