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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 Mathematica package 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.

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).

Quantum Workbook Cover
  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

Watch the 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

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.