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
| Name | Qubits | Matrix |
Circuit Symbol |
| CNOT / CX | 2 | 
|
|
| CY | 2 | 
|
|
| CZ | 2 | 
|
|
| Fredkin / CSWAP | 3 | 
|
|
| Hadamard H or H⊗1 | 1 | 
|
|
| Hadamard H⊗2 | 2 | 
|
|
| ID | 1 | 
|
|
| Measurement | 1 |
|
|
| Pauli X | 1 | 
|
|
| Pauli Y | 1 | 
|
|
| Pauli Z | 1 | 
|
|
|
1 | 
|
|
|
1 | 
|
|
|
1 | 
|
|
S =  |
1 | 
|
|
 =  =  |
1 | 
|
|
|
1 | 
|
|
| SWAP | 2 | 
|
|
T =  |
1 | 
|
|
 =  =  |
1 | 
|
|
| Toffoli / CCNOT | 3 | 
|
|
Appendix B
Symbols
B.1 Greek letters
| Name | Lowercase | Uppercase | ||||
| alpha | α | A | ||||
| beta | β | B | ||||
| gamma | γ | Γ | ||||
| delta | δ | Δ | ||||
| epsilon | ε | E | ||||
| zeta | ζ | Z | ||||
| eta | η | H | ||||
| theta | θ | Θ | ||||
| iota | ι | I | ||||
| kappa | κ | K | ||||
| lambda | λ | Λ | ||||
| mu | μ | M | ||||
| nu | ν | N | ||||
| xi | ξ | Ξ | ||||
| o | o | O | ||||
| pi | π | Π | ||||
| rho | ρ | P | ||||
| sigma | σ | Σ | ||||
| tau | τ | T | ||||
| upsilon | υ | Υ | ||||
| phi | ϕ | Φ | ||||
| chi | χ | X | ||||
| psi | ψ | Ψ | ||||
| omega | ω | Ω |
B.2 Mathematical notation and operations
| Short name | Notation |
Description |
| addition mod 2 | ⊕ |
Addition of integers or bits modulo 2. |
| adjoint | v† |
Complex transpose of vector v. |
| adjoint | A† |
Complex transpose of matrix A. |
| bra | ⟨v| |
Row vector in Dirac notation. |
| Cartesian product | V × W |
Cartesian product of vector spaces V and W. |
| ceiling | ⌈x⌉ |
Smallest integer greater than or equal to x. |
| complex numbers | C |
Complex numbers. |
| conjugate | z |
Complex conjugate of z. |
| direct sum | V ⊕ W |
Direct sum of vector spaces V and W. |
| dot product | v · w |
Dot product of vectors v and w. |
| e | e |
Base of the natural logarithms. |
| floor | ⌊x⌋ |
Largest integer less than or equal to x. |
| i | i = √−1 |
Square root of −1. |
| inner product | ⟨v | w⟩ |
Inner product of a bra and a ket in Dirac notation. |
| integers | Z |
Integers. |
| ket | |v⟩ |
Column vector in Dirac notation. |
| logarithm | log10 |
Base 10 logarithm. |
| logarithm | log2 |
Base 2 logarithm. |
| logarithm | log |
Natural logarithm. |
| natural numbers | N |
Natural numbers. |
| outer product | |v⟩⟨w| |
Outer product of a ket and a bra in Dirac notation. |
| product | 
|
Product f(k) × f(k+1) × ··· × f(n). |
| rationals | Q |
Rational numbers. |
| reals | R |
Real numbers. |
| summation | 
|
Sum f(k) + f(k+1) + ··· + f(n). |
| tensor product | |v⟩ ⊗ |w⟩ |
Tensor product of kets |v⟩ and |w⟩. |
| tensor product | v ⊗ w |
Tensor product of vectors v and w. |
| tensor product | A ⊗ B |
Tensor product of matrices A and B. |
| tensor product | V ⊗ W |
Tensor product of vector spaces V and W. |
| transpose | vT |
Transpose of vector v. |
| transpose | AT |
Transpose of matrix A. |
| vector | v |
Vector v. |
| whole numbers | W |
Whole numbers. |
Appendix C
Notices
C.1 Creative Commons Attribution 3.0 Unported (CC BY 3.0)
You are free to:
- Share – copy and redistribute the material in any medium or format
- Adapt – remix, transform, and build upon the material for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions – You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
C.2 Creative Commons Attribution-NoDerivs 2.0 Generic (CC BY-ND 2.0)
You are free to:
- Share – copy and redistribute the material in any medium or format for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- NoDerivatives —- If you remix, transform, or build upon the material, you may not distribute the modified material.
- No additional restrictions – You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
C.3 Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
You are free to:
- Share – copy and redistribute the material in any medium or format.
- Adapt – remix, transform, and build upon the material for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- ShareAlike – If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions – You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
C.4 Los Alamos National Laboratory
‘‘Unless otherwise indicated, this information has been authored by an employee or employees of the Los Alamos National Security, LLC (LANS), operator of the Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396 with the U.S. Department of Energy. The U.S. Government has rights to use, reproduce, and distribute this information. The public may copy and use this information without charge, provided that this Notice and any statement of authorship are reproduced on all copies. Neither the Government nor LANS makes any warranty, express or implied, or assumes any liability or responsibility for the use of this information.’’
C.5 Trademarks
- IBM, IBM Q, IBM Q Experience, and IBM Q Network are registered trademarks of the International Business Machines Corporation. IBM Q System One is a trademark of the International Business Machines Corporation.
- MATLAB is a registered trademark of The MathWorks, Inc.
- Mathematica is a registered trademark of Wolfram Research, Inc.
- Polaroid is a registered trademark of Polaroid Corporation.
- Python is a registered trademark of the Python Software Foundation.
- Wikipedia is a registered trademark of the Wikimedia Foundation, Inc.
Appendix D
Production Notes
The source content for this book was written in LATEX markup. I used many packages including amsmath, amssymb, biblatex, bookmark, ccicons, enumitem, framed, geometry, graphicx, hyperref, listings, minitoc, multicol, tcolorbox, and xifthen. Information about these packages is available at CTAN, the Comprehensive TEX Archive Network.
The diagrams and graphs were created with pgf/tikz, its libraries, and associated packages such as circuitikz. I am especially indebted to Alastair Kay for his brilliant quantikz package. All quantum circuits were created using this package.
I prepared the text in the open source Visual Studio Code editor from Microsoft and others. James Yu’s LaTeX Workshop extension made creating this book much easier. tex4ht and make4ht were used with custom Python and sed scripts to produce the eBook.
Files were stored in Dropbox folders and version control was handled by git and github.
If you cite this book with BibTeX, please use
AUTHOR = {Sutor, Robert S.},
PUBLISHER = {Packt Publishing},
DATE = {2019},
EDITION = {1},
ISBN = {978-1-83882-736-6},
TITLE = {Dancing with Qubits},
SUBTITLE = {How quantum computing works and how it can change the world}
}