Compact Representations for the Design of Quantum Logic

  • Philipp Niemann
  • Robert Wille

Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Introduction and Background

    1. Front Matter
      Pages 1-1
    2. Philipp Niemann, Robert Wille
      Pages 3-10
    3. Philipp Niemann, Robert Wille
      Pages 11-19
  3. Representation of Quantum Functionality

    1. Front Matter
      Pages 21-21
    2. Philipp Niemann, Robert Wille
      Pages 23-34
    3. Philipp Niemann, Robert Wille
      Pages 35-58
    4. Philipp Niemann, Robert Wille
      Pages 59-63
  4. Design of Quantum Logic

    1. Front Matter
      Pages 65-65
    2. Philipp Niemann, Robert Wille
      Pages 67-77
    3. Philipp Niemann, Robert Wille
      Pages 79-105
    4. Philipp Niemann, Robert Wille
      Pages 107-117
    5. Philipp Niemann, Robert Wille
      Pages 119-120
  5. Back Matter
    Pages 121-125

About this book


This book discusses modern approaches and challenges of computer-aided design (CAD) of quantum circuits with a view to providing compact representations of quantum functionality. Focusing on the issue of quantum functionality, it presents Quantum Multiple-Valued Decision Diagrams (QMDDs – a means of compactly and efficiently representing and manipulating quantum logic. For future quantum computers, going well beyond the size of present-day prototypes, the manual design of quantum circuits that realize a given (quantum) functionality on these devices is no longer an option. In order to keep up with the technological advances, methods need to be provided which, similar to the design and synthesis of conventional circuits, automatically generate a circuit description of the desired functionality. To this end, an efficient representation of the desired quantum functionality is of the essence. While straightforward representations are restricted due to their (exponentially) large matrix descriptions and other decision diagram-like structures for quantum logic suffer from not comprehensively supporting typical characteristics, QMDDs employ a decomposition scheme that more naturally models quantum systems. As a result, QMDDs explicitly support quantum-mechanical effects like phase shifts and are able to take more advantage of corresponding redundancies, thereby allowing a very compact representation of relevant quantum functionality composed of dozens of qubits. This provides the basis for the development of sophisticated design methods as shown for quantum circuit synthesis and verification.


Quantum computation Boolean logic Binary Decision Diagrams Quantum Decision Diagrams QMDD Quantum circuit simulation

Authors and affiliations

  • Philipp Niemann
    • 1
  • Robert Wille
    • 2
  1. 1.Department for Cyber-Physical SystemsGerman Research Center for Artificial Intelligence (DFKI)BremenGermany
  2. 2.Institute for Integrated CircuitsJohannes Kepler University LinzLinzAustria

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-63723-5
  • Online ISBN 978-3-319-63724-2
  • Series Print ISSN 2191-5423
  • Series Online ISSN 2191-5431
  • Buy this book on publisher's site
Industry Sectors
IT & Software
Energy, Utilities & Environment