Book Image

Quantum Chemistry and Computing for the Curious

By : Alex Khan, Keeper L. Sharkey, Alain Chancé
Book Image

Quantum Chemistry and Computing for the Curious

By: Alex Khan, Keeper L. Sharkey, Alain Chancé

Overview of this book

Explore quantum chemical concepts and the postulates of quantum mechanics in a modern fashion, with the intent to see how chemistry and computing intertwine. Along the way you’ll relate these concepts to quantum information theory and computation. We build a framework of computational tools that lead you through traditional computational methods and straight to the forefront of exciting opportunities. These opportunities will rely on achieving next-generation accuracy by going further than the standard approximations such as beyond Born-Oppenheimer calculations. Discover how leveraging quantum chemistry and computing is a key enabler for overcoming major challenges in the broader chemical industry. The skills that you will learn can be utilized to solve new-age business needs that specifically hinge on quantum chemistry

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Table of Contents (14 chapters)
Preface
Preface
Readers we target
A fast path to using quantum chemistry
Quantum chemistry
How to navigate the book
To get the most out of this book
Download the example code files
Conventions used
Get in touch
References
Share Your Thoughts
1
Chapter 1: Introducing Quantum Concepts
Chapter 1: Introducing Quantum Concepts
Technical requirements
1.1. Understanding the history of quantum chemistry and mechanics
1.2. Particles and matter
1.3. Quantum numbers and quantization of matter
1.4. Light and energy
1.5. A brief history of quantum computation
1.6. Complexity theory insights
Summary
Questions
References
Free Chapter
2
Chapter 2: Postulates of Quantum Mechanics
Chapter 2: Postulates of Quantum Mechanics
Technical requirements
2.1. Postulate 1 – Wave functions
2.2. Postulate 2 – Probability amplitude
2.3. Postulate 3 – Measurable quantities and operators
2.4. Postulate 4 – Time-independent stationary states
2.5. Postulate 5 – Time evolution dynamics
Questions
Answers
References
3
Chapter 3: Quantum Circuit Model of Computation
Chapter 3: Quantum Circuit Model of Computation
Technical requirements
3.1. Qubits, entanglement, Bloch sphere, Pauli matrices
3.2. Quantum gates
3.3. Computation-driven interference
3.4. Preparing a permutation symmetric or antisymmetric state
References
4
Chapter 4: Molecular Hamiltonians
Chapter 4: Molecular Hamiltonians
Technical requirements
4.1. Born-Oppenheimer approximation
4.2. Fock space
4.3. Fermionic creation and annihilation operators
4.4. Molecular Hamiltonian in the Hartree-Fock orbitals basis
4.5. Basis sets
4.6. Constructing a fermionic Hamiltonian with Qiskit Nature
4.7. Fermion to qubit mappings
4.8. Constructing a qubit Hamiltonian operator with Qiskit Nature
Summary
Questions
References
5
Chapter 5: Variational Quantum Eigensolver (VQE) Algorithm
Chapter 5: Variational Quantum Eigensolver (VQE) Algorithm
Technical requirements
5.1. Variational method
5.2. Example chemical calculations
Summary
Questions
Answers
References
6
Chapter 6: Beyond Born-Oppenheimer
Chapter 6: Beyond Born-Oppenheimer
Technical requirements
6.1. Non-Born-Oppenheimer molecular Hamiltonian
6.2. Vibrational frequency analysis calculations
6.3. Vibrational spectra for ortho-para isomerization of hydrogen molecules
Summary
Questions
Answers
References
7
Chapter 7: Conclusion
Chapter 7: Conclusion
7.1. Quantum computing
7.2. Quantum chemistry
References
8
Chapter 8: References
Chapter 8: References
9
Chapter 9:Glossary
Chapter 9:Glossary
10
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Appendix A: Readying Mathematical Concepts
Appendix A: Readying Mathematical Concepts
Technical requirements
Notations used
Mathematical definitions
References
Appendix B: Leveraging Jupyter Notebooks on the Cloud
Appendix B: Leveraging Jupyter Notebooks on the Cloud
Jupyter Notebook
References
Appendix C: Trademarks
Appendix C: Trademarks
Why subscribe?

Technical requirements

A companion Jupyter notebook for this chapter can be downloaded from GitHub at https://github.com/PacktPublishing/Quantum-Chemistry-and-Computing-for-the-Curious, which has been tested in the Google Colab environment, which is free and runs entirely in the cloud, and in the IBM Quantum Lab environment. Please refer to Appendix B – Leveraging Jupyter Notebooks in the Cloud, for more information. The companion Jupyter notebook automatically installs the following list of libraries:

  • NumPy [NumPy], an open-source Python library that is used in almost every field of science and engineering
  • SciPy [SciPy], a free and open-source Python library used for scientific computing and technical computing

The companion Jupyter notebook does not include the installation of the Psi4 free and open source software for high-throughput quantum chemistry [Psi4_0], which we used to perform a simple calculation of the vibrational frequency analysis of the carbon...

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