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Dancing with Qubits

Dancing with Qubits


Quantum computing is making us change the way we think about computers. Quantum bits, a.k.a. qubits, can make it possible to solve problems that would otherwise be intractable with current computing technology.

Dancing with Qubits is a quantum computing textbook that starts with an overview of why quantum computing is so different from classical computing and describes several industry use cases where it can have a major impact. From there it moves on to a fuller description of classical computing and the mathematical underpinnings necessary to understand such concepts as superposition, entanglement, and interference. Next up is circuits and algorithms, both basic and more sophisticated. It then nicely moves on to provide a survey of the physics and engineering ideas behind how quantum computing hardware is built. Finally, the book looks to the future and gives you guidance on understanding how further developments will affect you.

Really understanding quantum computing requires a lot of math, and this book doesn't shy away from the necessary math concepts you'll need. Each topic is introduced and explained thoroughly, in clear English with helpful examples.

  • Cover
  • Title Page
  • Copyright
  • Dedication
  • Contributors
  • Contents
  • Preface
  • 1 Why Quantum Computing?
    • 1.1 The mysterious quantum bit
    • 1.2 Im awake!
    • 1.3 Why quantum computing is different
    • 1.4 Applications to artificial intelligence
    • 1.5 Applications to financial services
    • 1.6 What about cryptography?
    • 1.7 Summary
  • 2 Theyre Not Old, Theyre Classics
    • 2.1 Whats inside a computer?
    • 2.2 The power of two
    • 2.3 True or false?
    • 2.4 Logic circuits
    • 2.5 Addition, logically
    • 2.6 Algorithmically speaking
    • 2.7 Growth, exponential and otherwise
    • 2.8 How hard can that be?
    • 2.9 Summary
  • 3 More Numbers than You Can Imagine
    • 3.1 Natural numbers
    • 3.2 Whole numbers
    • 3.3 Integers
    • 3.4 Rational numbers
    • 3.5 Real numbers
    • 3.6 Structure
    • 3.7 Modular arithmetic
    • 3.8 Doubling down
    • 3.9 Complex numbers, algebraically
    • 3.10 Summary
  • 4 Planes and Circles and Spheres, Oh My
    • 4.1 Functions
    • 4.2 The real plane
    • 4.3 Trigonometry
    • 4.4 From Cartesian to polar coordinates
    • 4.5 The complex plane
    • 4.6 Real three dimensions
    • 4.7 Summary
  • 5 Dimensions
    • 5.1 R2 and C1
    • 5.2 Vector spaces
    • 5.3 Linear maps
    • 5.4 Matrices
    • 5.5 Matrix algebra
    • 5.6 Cartesian products
    • 5.7 Length and preserving it
    • 5.8 Change of basis
    • 5.9 Eigenvectors and eigenvalues
    • 5.10 Direct sums
    • 5.11 Homomorphisms
    • 5.12 Summary
  • 6 What Do You Mean Probably?
    • 6.1 Being discrete
    • 6.2 More formally
    • 6.3 Wrong again?
    • 6.4 Probability and error detection
    • 6.5 Randomness
    • 6.6 Expectation
    • 6.7 Markov and Chebyshev go to the casino
    • 6.8 Summary
  • 7 One Qubit
    • 7.1 Introducing quantum bits
    • 7.2 Bras and kets
    • 7.3 The complex math and physics of a single qubit
    • 7.4 A non-linear projection
    • 7.5 The Bloch sphere
    • 7.6 Professor Hadamard, meet Professor Pauli
    • 7.7 Gates and unitary matrices
    • 7.8 Summary
  • 8 Two Qubits, Three
    • 8.1 Tensor products
    • 8.2 Entanglement
    • 8.3 Multi-qubit gates
    • 8.4 Summary
  • 9 Wiring Up the Circuits
    • 9.1 So many gates
    • 9.2 From gates to circuits
    • 9.3 Building blocks and universality
    • 9.4 Arithmetic
    • 9.5 Welcome to Delphi
    • 9.6 Amplitude amplification
    • 9.7 Searching
    • 9.8 The Deutsch-Jozsa algorithm
    • 9.9 Simons algorithm
    • 9.10 Summary
  • 10 From Circuits to Algorithms
    • 10.1 Quantum Fourier Transform
    • 10.2 Factoring
    • 10.3 How hard can that be, again
    • 10.4 Phase estimation
    • 10.5 Order and period finding
    • 10.6 Shors algorithm
    • 10.7 Summary
  • 11 Getting Physical
    • 11.1 Thats not logical
    • 11.2 What does it take to be a qubit?
    • 11.3 Light and photons
    • 11.4 Decoherence
    • 11.5 Error correction
    • 11.6 Quantum Volume
    • 11.7 The software stack and access
    • 11.8 Simulation
    • 11.9 The cat
    • 11.10 Summary
  • 12 Questions about the Future
    • 12.1 Ecosystem and community
    • 12.2 Applications and strategy
    • 12.3 Access
    • 12.4 Software
    • 12.5 Hardware
    • 12.6 Education
    • 12.7 Resources
    • 12.8 Summary
  • Afterword
  • Appendices
    • Appendix A Quick Reference
      • A.1 Common kets
        • One qubit
          • Computational basis (Z)
          • Hadamard basis (X)
          • Circular basis (Y)
        • Two qubits
          • Computational basis
          • Bell state basis
      • A.2 Quantum gates and operations
    • Appendix B Symbols
      • B.1 Greek letters
      • B.2 Mathematical notation and operations
    • Appendix C Notices
      • C.1 Creative Commons Attribution 3.0 Unported (CC BY 3.0)
      • C.2 Creative Commons Attribution-NoDerivs 2.0 Generic (CC BY-ND 2.0)
      • C.3 Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
      • C.4 Los Alamos National Laboratory
      • C.5 Trademarks
    • Appendix D Production Notes
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