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by Robert S. Sutor
Dancing with Qubits
Cover
Title Page
Copyright
Dedication
Contributors
Contents
Preface
1 Why Quantum Computing?
1.1 The mysterious quantum bit
1.2 I’m 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 They’re Not Old, They’re Classics
2.1 What’s 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 Simon’s 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 Shor’s algorithm
10.7 Summary
11 Getting Physical
11.1 That’s 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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