A Quantum Playbook

This package contains two compilations of Mathematica(R) demonstrations. The first, Workbook Demonstrations, includes all demonstrations in "A Quantum Computation Workbook" (Springer, March 2022). The other, Playbook Demonstrations, is a collection of demonstrations of various topics in the field of quantum information systems, quatum many-body systems, and quantum spin systems. Users can try and modify the code themselves to build their own examples on the demonstrations and to experiment their fresh ideas.

The code in this package is based on Wolfram Language framework Q3. Q3 consists of tools and utilities that perform symbolic calculations and numerical simulations useful in the study of quantum information processing, quantum many-body systems, and quantum spin systems. With Q3, one can avoid many of the tedious calculations involved in various principles and theorems of quantum theory. Furthermore, numerous visualization and simulation tools can help deepen the understanding of core concepts.

NOTICE

The official Paclet name of this package has been changed to "QauntumMob/QuantumPlaybook" (previously, "QuantumPlaybook") following the convention of the Wolfram Language Paclet Repository. To load the package, use

Get["QuantumMob`QuantumPlaybook`"]

or

Needs["QuantumMob`QuantumPlaybook`"]

(usually it is autoloaded when needed). The primary context is now "QuantumMob`QuantumPlaybook`" (rather than previous "QuantumPlaybook`").

Installation

QuantumPlaybook provides a fully automatic installation and update. Please take a look at the Installation Guide for the instructions.

Workbook Demonstrations

This is a compilation of the demonstrations in "A Quantum Computation Workbook" (Springer, March 2022).

1. The Postulates of Quantum Mechanics
2. Quantum Computation: Overview (Full text of Chapter 2 in PDF)
3. Realizations of Quantum Computers
4. Quantum Algorithms
5. Quantum Decoherence
6. Quantum Error-Correction Codes
7. Quantum Information Theory

• Appendix A. Linear Algebra (available free of charge as Back Matter from the Springer Link)
• Appendix B. Superoperators (available free of charge as Back Matter from the Springer Link)
• Appendix C. Group Theory (available free of charge as Back Matter from the Springer Link)
• Appendix D. Mathematica Application Q3 (available free of charge as Back Matter from the Springer Link)
• Appendix E. Integrated Compilation of Demonstrations (available free of charge as Back Matter from the Springer Link)
• Appendix F. Solutions to Select Problems (available free of charge as Back Matter from the Springer Link)
• Bibliography (available free of charge as Back Matter from the Springer Link)
• Index (available free of charge as Back Matter from the Springer Link)

ERRATA: Unfortunately, the book has several typographical errors. Please check the errata for corrections.

BACK MATERIALS: All back materials including appendices, bibliography, and index are available in a single PDF file, free of charge from the Springer Link.

Playbook Demonstrations

Here is another compilation of demonstrations that have not been covered in detail or at all in "A Quantum Computation Workbook" (Springer, March 2022). This includes a wide range of topics from the field of quantum information systems, quantum many-body systems, and quantum spin systems.

• Partial Trace: Physical Meaning
• Non-Unitary Dynamics of Quantum States
• Transposition as a Supermap
• Addition of Numbers
• Measurement of Total Pauli Z
• Entanglement Distillation
• Lambda-Matter in a Cavity
• Symmetry Effects on Quantum Master Equations
• Transmon: Quantum Phase Model
• And many others

Demonstrations in YouTube Videos

The tutorials of Q3 for beginners are also available in YouTube videos. The notebook files below contain the demonstrations shown in the corresponding videos.

1. Q3: Install & Quick Start
2. Quantum Playbook
3. Qubits (Quantum Bits)
4. Quantum States
5. QuantumOpertators
6. Quantum Measurement
7. Quantum Circuits
8. Mathematica Cool Tips
9. Matrix Representation
10. Phase Operators
11. Single-Qubit Rotations
12. Schmidt Decomposition
13. The CNOT Gate 1: Elementary Properties
14. The CNOT Gate 2: Parity Measurement
15. Multi-Control NOT Gate
16. The CZ Gate
17. Controlled-Unitary Gates
18. More Mathematica Cool Tips
19. Controlled-Unitary Gates: Special Examples
20. Working in Different Bases
21. Working in Different Bases: Simple Way
22. Dyadic Products
23. Multi-Level Systems (Qudits)
24. Cavity QED Systems
25. Cavity QED Systems: Spectral Properties
26. Classical Oracle
27. Quantum Oracle: Definition
28. Quantum Oracle: Properties
29. Deutsch-Jozsa Algorithm
30. Bernstein-Vazirani Algorithm
31. Simon's Algorithm
32. Quantum Fourier Transform: Principle
33. Quantum Fourier Transform: Implementation
34. Controlled-Power Gate
35. Quantum Phase Estimation: Principle
36. Quantum Phase Estimation: Implementation
37. Mixed States
38. Partial Trace and Purification
39. Supermaps
40. Quantum Operations
41. Quantum Master Equation
42. Quantum Master Equation: Solution Method
43. Quantum Master Equation: Monte Carlo Method
44. Shor Code: Bit-Flip Errors
45. Shor Code: Phase-Flip Errors
46. Shor Code: General Errors
47. Gottesman-Knill Theorem
48. Clifford Circuits
49. Classical Entropy
50. Quantum Entropy

How to use

Once QuantumPlaybook is installed, put QuantumPlaybook in the search field of the Wolfram Documentation Center (Mathematica Help window). You will see the table of contents of the playbook.