DOCSLIB.ORG

Introduction to Quantum Computing and Its Applications to Cyber Security

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introduction to Quantum Computing and Its Applications to Cyber Security Introduction to Quantum Computing and its Applications to Cyber Security Raj Jain Washington University in Saint Louis Saint Louis, MO 63130 [email protected] These slides and audio/video recordings of this class lecture are at: http://www.cse.wustl.edu/~jain/cse570-19/ Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-1 Overview 1. What is a Quantum and Quantum Bit? 2. Matrix Algebra Review 3. Quantum Gates: Not, And, or, Nand 4. Applications of Quantum Computing 5. Quantum Hardware and Programming Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-2 What is a Quantum? Quantization: Analog to digital conversion Quantum = Smallest discrete unit Quantum Wave Theory: Light is a wave. It has a frequency, phase, amplitude Quantum Mechanics: Light behaves like discrete packets of energy that can be absorbed and released Wave Photon = One quantum of light energy Photon Photons can move an electron from one energy level to next higher level Photons are released when an electron moves from one level to lower energy level Electrons Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-3 Probabilistic Behavior Young’s Double-Slit Experiment 1801 Photons The two waves exiting the slits interfere. Interference is constructive at some spots and destructive at others ⇒ Probabilistic Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-4 Quantum Bits 1. Computing bit is a binary scalar: 0 or 1 10 or 2. Quantum bit (Qubit) is a 2×1 vector: 01 3. Vector elements of Qubits are complex numbers x+iy 4. Modulus of a complex Number |x+= iy | ( x + iy )( x− i y ) =xy22+ Conjugate Example: | (1+ 2|) = (1+= 2ii ) (1−= 2i) 1+ 4 5 5. Probability of each element in a qubit vector is proportional to its modulus squared a Pa=||||22 /(| a2 + | a ) 0 ⇒ 0 01 222 a1 Pa=|1 ||| /(| a01 + | a ) 1+ 2ii |1 + 2 | (1+− 2ii )(1 2 ) 5 5/(5+= 2) 5/7 ⇒ = = ⇒=P 1−ii |1 − | (1−+ii )(1 ) 2 2/(5+= 2) 2/7 Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-5 Polar Representation Complex numbers in polar coordinates: (x+= iy) reiθ = r( cos()θθ + isin ()) r y 22 θ r= xy + x θ = tan−1(/ y x) Imaginary 2π = 360o (-1+i) (1+i) π o 1 1 /4=45 Real -1 1 -1 C 12+ ieiπ /4 2( cos(ππ / 4)+ i sin( / 4)) = = −+ 3π /4 1 i 2e 2( cos(3ππ / 4)+ i sin(3 / 4)) Exercise: Find the complex and polar representation of C Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-6 Qubit Interpretation [Source: Johnston, et al. 2019] If a single photon is emitted from the source, the photon reaches position A or B with some probability ⇒ Photon has a superposition (rather than position) Each position has a different path length and, therefore, different amplitude and phase Ref: E. R. Johnston, N. Harrigan, and M. Gimeno-Segovia, "Programming Quantum Computers," O'reilly, 2019, ISBN:9781492039686, 320 pp. Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-7 Bra-Ket Notation The vector ψ is denoted in bra-kets | ψ > Brackets: { }, [ ], < > Bra <a| Ket |a> Example: Ket-zero and ket-one 10 =>=> |0 |1 01 Bra is the transpose of the complex-conjugate of a Ket. Example: Bra-zero and Bra-one [1 0] = <0 | [0 1] = <1| Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-8 Matrix Multiplication Matrix multiplication ×: bb aaa 01 01 00 01 02 × bb10 11 aaa10 11 12 bb20 21 aaa00b 00++ 01b 10 02 b 20 a 00 bbb 01 ++aa 01 11 02 21 = a bbb++aa+ aabbb + a 10 00 11 10 12 20 10 01 11 11 12 21 Example: 01 111 101 11×= 21 2 11 1 00 000 3×2 2×3 3×3 Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-9 Tensor Product Tensor Product ⊗ : m×n ⊗ k×l results in mk×nl matrix bbb aa 00 01 02 = 00 01 = A Bbbb10 11 12 aa10 11 bbb20 21 22 bbb00 01 02 bbb00 01 02 abbb00 10 11 12 abbb 01 10 11 12 bbb20 21 22 bbb20 21 22 AB⊗= bbb00 01 02 bbb00 01 02 abbb10 10 11 12 abb 11 10 11b 12 bbb20 21 22 bbb20 21 22 aaaaaa00bbbbbb 00 00 01 00 02 01 00 01 01 01 02 aaaaaa00bbbbbb 10 00 11 00 12 01 10 01 11 01 12 aaaaaabbbbbb = 00 20 00 21 00 22 01 20 01 21 01 22 aaaaaa10bb 00 10 01 10b 02 11 b 00 11 bb 01 11 02 aabba bbbbaaa 10 10 10 11 10 12 11 10 11 11 11 12 aa10b 20a 10b 21a 10b 22aa 11b 20 11b 21 11b 22 Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-10 Tensor Product (Cont) b Example 1: 00 a00b 00 a00 b 10 a00b 10 a 00 bb a b 00 00 10 00 aa10 ⊗=10 = b bab 10 10 10 10 a20 a b b00 20 00 a 20 a b b10 20 10 3×1 2×1 6×1 01 000101 Example 2: ⊗=[101] 11 1 01101 2×2 1×3 2×6 Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-11 Multiple Qubits and QuBytes 10 One Qbit: | 0>= |1 >= 01 10 00 110 1 0 0 Two Qbits: |00>= |0 >⊗ | 0 > = ⊗ = |01 >= |10 >= |11 >= 000 0 1 0 Tensor Product 00 01 1 0 0000 00 0 1 0000 00 0 0 1000 00 0 0 01 0 000 Three Qbits: 0 0 00 1 0 00 0 0 00 0 1 00 0 0 0000 10 0 0 0000 01 | 000>> | 001 | 010 >>>>>> | 011 | 100 | 101 | 110 | 111 In a k-qubit register, each of the 2k positions can be any complex number QuByte=8-Qubits = 256-element vector Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-12 Homework 19A Given two matrices: 11+ i 1 AB= = 10− ii Compute: A× BA, ⊗ B Compute the probabilities of each element of AB× Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-13 Quantum Gates 1. Quantum NOT Gate 2. Quantum AND Gate 3. Quantum OR Gate 4. Quantum NAND Gate 5. Quantum √NOT Gate Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-14 Quantum NOT Gate NOT: 01 NOT = 10 01 0 1 01 1 ? ×= ×= 10 1 0 10 0 ? NOT |1>= |0 > NOT |0 >= |? > Exercise: Fill in the ?’s Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-15 Quantum AND Gate AND: 1110 AND = 0001 1000 1110 0 1 0 0 1 1 1 ? × = 0001 0 0 1 0 0 0 0 ? 0001 AND | 00>>>> | 01 |10 |11 = |0> |0> |0> |?> 2×4 4×1 2×1 Exercise: Fill in the ?’s Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-16 Quantum OR Gate OR: 1000 OR = 0111 1000 1000 0 1 0 0 1 0 0 0 × = 0111 0 0 1 0 0 1 1 1 0001 OR | 00>>>> | 01 |10 |11 = |0> |1> |1> |1> Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-17 Quantum NAND Gate NAND: 0001 NAND = 1110 1000 0001 0 1 0 0 0 0 0 1 × = 1110 0 0 1 0 1 1 1 0 0001 NAND | 00>>>> | 01 |10 |11 = |1> |1> |1> |0> Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-18 Quantum √NOT Gate √NOT: √NOT ×√NOT = NOT 1 11− NOT = 2 11 111111−− 0 1 11 − 1 1 ×= ×= 222211 1 1 11 0 1 |1> |0> 1111− −− 1 1 11 11 − 1 0 × = ×= 2211 1 0 22 11 1 1 |0> |1> Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-19 Controlled NOT Gate CNOT: If the control bit is 0, no change to the 2nd bit If control bit is 1, the 2nd bit is complemented • 1000 ⊕ 0100 CNOT = 0001 0010 1000 1 0 0 0 1 0 0 0 0100 0 1 0 0 0 1 0 0 × = 0001 0 0 1 0 0 0 0 1 00100001 001 0 CNOT | 00>>>> | 01 |10 |11 = |00> |01> |11> |10> Controlled NOT gate can be used to produce two bits that are entangled ⇒ Two bits behave similarly even if far apart ⇒ Can be used for teleportation of information Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-20 Quantum Gates: Summary 01 1110 NOT= AND= 10 0001 Classical 1000 0001 OR= NAND= 0111 1110 1000 1 1− 1 0100 NOT= CNOT= Non-Classical 2 1 1 0001 0010 The first 4 gates above are similar to the classical gates. The last two are non-classical gate. There are many other classical/non-classical quantum gates, e.g., Rotate, Copy, Read, Write, … Using such gates one can design quantum circuits Washington University in St. Louis http://www.cse.wustl.edu/~jain/ ©2019 Raj Jain 19-21 Quantum Applications It has been shown that quantum computation makes several problems easy that are hard currently.
Load more

Recommended publications
  • Quantum Computing: Principles and Applications
    Journal of International Technology and Information Management Volume 29 Issue 2 Article 3 2020 Quantum Computing: Principles and Applications Yoshito Kanamori University of Alaska Anchorage, [email protected] Seong-Moo Yoo University of Alabama in Huntsville, [email protected] Follow this and additional works at: https://scholarworks.lib.csusb.edu/jitim Part of the Communication Technology and New Media Commons, Computer and Systems Architecture Commons, Information Security Commons, Management Information Systems Commons, Science and Technology Studies Commons, Technology and Innovation Commons, and the Theory and Algorithms Commons Recommended Citation Kanamori, Yoshito and Yoo, Seong-Moo (2020) "Quantum Computing: Principles and Applications," Journal of International Technology and Information Management: Vol. 29 : Iss. 2 , Article 3. Available at: https://scholarworks.lib.csusb.edu/jitim/vol29/iss2/3 This Article is brought to you for free and open access by CSUSB ScholarWorks. It has been accepted for inclusion in Journal of International Technology and Information Management by an authorized editor of CSUSB ScholarWorks. For more information, please contact [email protected]. Journal of International Technology and Information Management Volume 29, Number 2 2020 Quantum Computing: Principles and Applications Yoshito Kanamori (University of Alaska Anchorage) Seong-Moo Yoo (University of Alabama in Huntsville) ABSTRACT The development of quantum computers over the past few years is one of the most significant advancements in the history of quantum computing. D-Wave quantum computer has been available for more than eight years. IBM has made its quantum computer accessible via its cloud service. Also, Microsoft, Google, Intel, and NASA have been heavily investing in the development of quantum computers and their applications.
    [Show full text]
  • Arxiv:2103.11307V1 [Quant-Ph] 21 Mar 2021
    QuClassi: A Hybrid Deep Neural Network Architecture based on Quantum State Fidelity Samuel A. Stein1,4, Betis Baheri2, Daniel Chen3, Ying Mao1, Qiang Guan2, Ang Li4, Shuai Xu3, and Caiwen Ding5 1 Computer and Information Science Department, Fordham University, {sstein17, ymao41}@fordham.edu 2 Department of Computer Science, Kent State University, {bbaheri, qguan}@kent.edu 3 Computer and Data Sciences Department,Case Western Reserve University, {txc461, sxx214}@case.edu 4 Pacific Northwest National Laboratory (PNNL), Email: {samuel.stein, ang.li}@pnnl.gov 5 University of Connecticut, Email: [email protected] Abstract increasing size of data sets raises the discussion on the future of DL and its limitations [42]. In the past decade, remarkable progress has been achieved in In parallel with the breakthrough of DL in the past years, deep learning related systems and applications. In the post remarkable progress has been achieved in the field of quan- Moore’s Law era, however, the limit of semiconductor fab- tum computing. In 2019, Google demonstrated Quantum rication technology along with the increasing data size have Supremacy using a 53-qubit quantum computer, where it spent slowed down the development of learning algorithms. In par- 200 seconds to complete a random sampling task that would allel, the fast development of quantum computing has pushed cost 10,000 years on the largest classical computer [5]. Dur- it to the new ear. Google illustrates quantum supremacy by ing this time, quantum computing has become increasingly completing a specific task (random sampling problem), in 200 available to the public. IBM Q Experience, launched in 2016, seconds, which is impracticable for the largest classical com- offers quantum developers to experience the state-of-the-art puters.
    [Show full text]
  • Off-The-Shelf Components for Quantum Programming and Testing
    Off-the-shelf Components for Quantum Programming and Testing Cláudio Gomesa, Daniel Fortunatoc, João Paulo Fernandesa and Rui Abreub aCISUC — Departamento de Engenharia Informática da Universidade de Coimbra, Portugal bFaculty of Engineering of the University of Porto, Portugal cInstituto Superior Técnico, University of Lisbon, Portugal Abstract In this position paper, we argue that readily available components are much needed as central contribu- tions towards not only enlarging the community of quantum computer programmers, but also in order to increase their efficiency and effectiveness. We describe the work we intend to do towards providing such components, namely by developing and making available libraries of quantum algorithms and data structures, and libraries for testing quantum programs. We finally argue that Quantum Computer Programming is such an effervescent area that synchronization efforts and combined strategies within the community are demanded to shorten the time frame until quantum advantage is observed and can be explored in practice. Keywords Quantum Computing, Software Engineering, Reusable Components 1. Introduction There is a large body of compelling evidence that Computation as we have known and used for decades is under challenge. As new models for computation emerge, its limits are being pushed beyond what pragmatically had been seen in practice. In this line, Quantum Computing (QC) has received renewed worldwide attention. Having its foundations been thoroughly studied, mainly from the point of view of its physical implementation, their potential has, even if preliminarily, is currently being witnessed. A quantum computer can potentially solve various problems that a classical computer cannot solve efficiently; this is known as Quantum Supremacy.
    [Show full text]
  • Student User Experience with the IBM Qiskit Quantum Computing Interface
    Proceedings of Student-Faculty Research Day, CSIS, Pace University, May 4th, 2018 Student User Experience with the IBM QISKit Quantum Computing Interface Stephan Barabasi, James Barrera, Prashant Bhalani, Preeti Dalvi, Ryan Kimiecik, Avery Leider, John Mondrosch, Karl Peterson, Nimish Sawant, and Charles C. Tappert Seidenberg School of CSIS, Pace University, Pleasantville, New York Abstract - The field of quantum computing is rapidly Schrödinger [11]. Quantum mechanics states that the position expanding. As manufacturers and researchers grapple with the of a particle cannot be predicted with precision as it can be in limitations of classical silicon central processing units (CPUs), Newtonian mechanics. The only thing an observer could quantum computing sheds these limitations and promises a know about the position of a particle is the probability that it boom in computational power and efficiency. The quantum age will be at a certain position at a given time [11]. By the 1980’s will require many skilled engineers, mathematicians, physicists, developers, and technicians with an understanding of quantum several researchers including Feynman, Yuri Manin, and Paul principles and theory. There is currently a shortage of Benioff had begun researching computers that operate using professionals with a deep knowledge of computing and physics this concept. able to meet the demands of companies developing and The quantum bit or qubit is the basic unit of quantum researching quantum technology. This study provides a brief information. Classical computers operate on bits using history of quantum computing, an in-depth review of recent complex configurations of simple logic gates. A bit of literature and technologies, an overview of IBM’s QISKit for information has two states, on or off, and is represented with implementing quantum computing programs, and two a 0 or a 1.
    [Show full text]
  • Introduction to Quantum Programming
    Introduction to Quantum Programming Jaros law Miszczak IITiS PAN April 27, 2018 QIPLSIGML|Machine Learning meets Quantum Computation Introduction to Quantum Programming 1/40 Our goals Quantum programming Manipulation of quantum gates Programming QRAM High-level programming What next? Q? Introduction to Quantum Programming 2/40 I Introduce various approaches to quantum programming. I Write some code. Our goals I Understand the difference between quantum and classical programming. Introduction to Quantum Programming 3/40 I Write some code. Our goals I Understand the difference between quantum and classical programming. I Introduce various approaches to quantum programming. Introduction to Quantum Programming 3/40 Our goals I Understand the difference between quantum and classical programming. I Introduce various approaches to quantum programming. I Write some code. Introduction to Quantum Programming 3/40 Our goals I Understand the difference between quantum and classical programming. I Introduce various approaches to quantum programming. I Write some code. ( Talk is cheap. Show me the quantum code.) ≡ Introduction to Quantum Programming 3/40 Quantum programming Introduction to Quantum Programming 4/40 Quantum programming What is quantum programming? Quantum programming is a process that leads from an original formulation of a computing problem to executable quantum computer programs. Introduction to Quantum Programming 5/40 I The process of preparing programs for a quantum computer is especially attractive because it not only can be economically and scientifically rewarding, it can also be an aesthetic experience much like composing poetry or music. I Only the modern quantum computer has made quantum programming both challenging and relevant. Quantum programming What is quantum programming? I The only way to learn a new quantum programming language is by writing programs in it.
    [Show full text]
  • High Energy Physics Quantum Information Science Awards Abstracts
    High Energy Physics Quantum Information Science Awards Abstracts Towards Directional Detection of WIMP Dark Matter using Spectroscopy of Quantum Defects in Diamond Ronald Walsworth, David Phillips, and Alexander Sushkov Challenges and Opportunities in Noise‐Aware Implementations of Quantum Field Theories on Near‐Term Quantum Computing Hardware Raphael Pooser, Patrick Dreher, and Lex Kemper Quantum Sensors for Wide Band Axion Dark Matter Detection Peter S Barry, Andrew Sonnenschein, Clarence Chang, Jiansong Gao, Steve Kuhlmann, Noah Kurinsky, and Joel Ullom The Dark Matter Radio‐: A Quantum‐Enhanced Dark Matter Search Kent Irwin and Peter Graham Quantum Sensors for Light-field Dark Matter Searches Kent Irwin, Peter Graham, Alexander Sushkov, Dmitry Budke, and Derek Kimball The Geometry and Flow of Quantum Information: From Quantum Gravity to Quantum Technology Raphael Bousso1, Ehud Altman1, Ning Bao1, Patrick Hayden, Christopher Monroe, Yasunori Nomura1, Xiao‐Liang Qi, Monika Schleier‐Smith, Brian Swingle3, Norman Yao1, and Michael Zaletel Algebraic Approach Towards Quantum Information in Quantum Field Theory and Holography Daniel Harlow, Aram Harrow and Hong Liu Interplay of Quantum Information, Thermodynamics, and Gravity in the Early Universe Nishant Agarwal, Adolfo del Campo, Archana Kamal, and Sarah Shandera Quantum Computing for Neutrino‐nucleus Dynamics Joseph Carlson, Rajan Gupta, Andy C.N. Li, Gabriel Perdue, and Alessandro Roggero Quantum‐Enhanced Metrology with Trapped Ions for Fundamental Physics Salman Habib, Kaifeng Cui1,
    [Show full text]
  • Towards a Quantum Programming Language
    The final version of this paper appeared in Math. Struct. in Comp. Science 14(4):527-586, 2004 Towards a Quantum Programming Language P E T E R S E L I N G E R y Department of Mathematics and Statistics University of Ottawa Ottawa, Ontario K1N 6N5, Canada Email: [email protected] Received 13 Nov 2002, revised 7 Jul 2003 We propose the design of a programming language for quantum computing. Traditionally, quantum algorithms are frequently expressed at the hardware level, for instance in terms of the quantum circuit model or quantum Turing machines. These approaches do not encourage structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types. The language is functional in nature, statically typed, free of run-time errors, and it has an interesting denotational semantics in terms of complete partial orders of superoperators. 1. Introduction Quantum computation is traditionally studied at the hardware level: either in terms of gates and circuits, or in terms of quantum Turing machines. The former viewpoint emphasizes data flow and neglects control flow; indeed, control mechanisms are usually dealt with at the meta-level, as a set of instructions on how to construct a parameterized family of quantum circuits. On the other hand, quantum Turing machines can express both data flow and control flow, but in a sense that is sometimes considered too general to be a suitable foundation for implementations of future quantum computers.
    [Show full text]
  • Quantum Computing in the Automotive Industry
    Quantum Computing in the Automotive Industry Applications, Opportunities, Challenges and Legal Risks Contents Introduction 1 Possible applications or use cases in the automotive industry 2 Quantum Computing 3 Quantum Physics 4 Quantum Physics 6 Quantum Computing 8 Quantum Error Correction (QEC) 10 Legal Implications and Risks of Quantum Computing 11 Introduction Quantum Computing is a new buzzword1 – generally in the IT and high-tech industries and also already in the automotive industry2. In fact, according to McKinsey, 10% of all potential use cases for quantum computing could benefit the automotive industry, with a high impact to be expected by 20253. Quantum computing will have real implications, This is possible because quantum computing builds benefits and risks for the automotive industry. on the advantages of the laws of quantum physics, More generally, it is a disruptive technology as where subatomic particles can exist in more than regards high performance computers and super- one state at any one time; their behaviour causes computing processes. quantum computers to be more powerful, efficient and faster than the conventional digital A key advantage of quantum computing is that its supercomputers. computing processes are much faster as they are no longer based on algorithms and mathematics, but on quantum physics (see below III. and IV.); quantum computers are able to do several calculations at the same time (in contrast to traditional computers) which make them exponentially faster. 1 From quantum advantage (Digitale Welt 2/2021, p. 86) February 2021, p. 8. https://www.bosch.com/stories/how- https://digitaleweltmagazin.de/d/magazin/DW_21_02.pdf and quantum-computing-can-tilt-the-computational-landscape/ Google’s alleged Quantum Supremacy via the EU Commission’s 2 A very easy to read, almost colloquial but still informative Quantum Technologies Flagship https://digital- introduction is by Dr.
    [Show full text]
  • Quantum Transpiler Optimization: on the Development, Implementation, and Use of a Quantum Research Testbed
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by AFTI Scholar (Air Force Institute of Technology) Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-2020 Quantum Transpiler Optimization: On the Development, Implementation, and Use of a Quantum Research Testbed Brandon K. Kamaka Follow this and additional works at: https://scholar.afit.edu/etd Part of the Computer Sciences Commons Recommended Citation Kamaka, Brandon K., "Quantum Transpiler Optimization: On the Development, Implementation, and Use of a Quantum Research Testbed" (2020). Theses and Dissertations. 3590. https://scholar.afit.edu/etd/3590 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. Quantum Transpiler Optimization: On the Development, Implementation, and Use of a Quantum Research Testbed THESIS Brandon K Kamaka AFIT-ENG-MS-20-M-029 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a
    [Show full text]
  • Logic Synthesis for Quantum Computing Mathias Soeken, Martin Roetteler, Nathan Wiebe, and Giovanni De Micheli
    1 Logic Synthesis for Quantum Computing Mathias Soeken, Martin Roetteler, Nathan Wiebe, and Giovanni De Micheli Abstract—Today’s rapid advances in the physical implementa- 1) Quantum computers process qubits instead of classical tion of quantum computers call for scalable synthesis methods to bits. A qubit can be in superposition and several qubits map practical logic designs to quantum architectures. We present can be entangled. We target purely Boolean functions as a synthesis framework to map logic networks into quantum cir- cuits for quantum computing. The synthesis framework is based input to our synthesis algorithms. At design state, it is on LUT networks (lookup-table networks), which play a key sufficient to assume that all input values are Boolean, role in state-of-the-art conventional logic synthesis. Establishing even though entangled qubits in superposition are even- a connection between LUTs in a LUT network and reversible tually acted upon by the quantum hardware. single-target gates in a reversible network allows us to bridge 2) All operations on qubits besides measurement, called conventional logic synthesis with logic synthesis for quantum computing—despite several fundamental differences. As a result, quantum gates, must be reversible. Gates with multiple our proposed synthesis framework directly benefits from the fanout known from classical circuits are therefore not scientific achievements that were made in logic synthesis during possible. Temporarily computed values must be stored the past decades. on additional helper qubits, called ancillae. An intensive We call our synthesis framework LUT-based Hierarchical use of intermediate results therefore increases the qubit Reversible Logic Synthesis (LHRS).
    [Show full text]
  • Programming Gate-Based Hardware Quantum Computers for Music
    DOI https://doi.org/10.2298/MUZ1824021K UDC 789.983 004.9:78 Programming Gate-based Hardware Quantum Computers for Music Alexis Kirke1 University of Plymouth, School of Humanities and Performing Arts Received: 17 April 2018 Accepted: 7 May 2018 Original scientific paper Abstract There have been significant attempts previously to use the equations of quantum mechanics for generating sound, and to sonify simulated quantum processes. For new forms of computation to be utilized in computer music, eventually hardware must be utilized. This has rarely happened with quantum computer music. One reason for this is that it is currently not easy to get access to such hardware. A second is that the hardware available requires some understanding of quantum computing theory. Tis paper moves forward the process by utilizing two hardware quantum computation systems: IBMQASM v1.1 and a D-Wave 2X. It also introduces the ideas behind the gate-based IBM system, in a way hopefully more accessible to computer- literate readers. Tis is a presentation of the frst hybrid quantum computer algorithm, involving two hardware machines. Although neither of these algorithms explicitly utilize the promised quantum speed-ups, they are a vital frst step in introducing QC to the musical feld. Te article also introduces some key quantum computer algorithms and discusses their possible future contribution to computer music. Keywords: quantum computer music, algorithms, D-Wave Introduction: Quantum Computing Why Quantum Computing? The typical answer is speed. Quantum mechanics models the world by considering a physical state as a sum of all its possible configu- rations. For example, the physical state of an electron is modeled as a weighted sum of a large number of vectors (called eigenvectors), each of which represents somet- hing that could possibly happen in the physical world.
    [Show full text]
  • Quantum Programming Languages: Survey and Bibliography 3
    Under consideration for publication in Math. Struct. in Comp. Science Quantum Programming Languages Survey and Bibliography S i m o n J. G a y Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK Email: [email protected] Received 13 October 2005; Revised 24 March 2006 The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechanics, and the design of compilers for quantum programming languages. This article justifies the study of quantum programming languages, presents the basics of quantum computing, surveys the literature in quantum programming languages, and indicates directions for future research. 1. Introduction Feynman (1982) suggested that constructing computers based on the principles of quan- tum mechanics might enable the quantum systems of interest to physicists to be efficiently simulated, whereas this seemed to be very difficult with classical computers. Deutsch (1985) investigated the possible computational power of physically realizable comput- ers, and formulated a quantum version of the Turing machine. Shor (1994) demonstrated that two important practical problems—factorizing integers and the “discrete logarithm” problem—could be solved efficiently by quantum computers. Grover (1996) showed that database search could also be made more efficient by the use of quantum computers. Since then, a substantial literature has developed in quantum algorithms and quantum complexity theory. Another important theme in quantum computing has been the development of quan- tum cryptographic techniques, going back to the work of Bennett and Brassard (1984) which in turn built on work, not published until several years after its conception, by Wiesner (1983).
    [Show full text]