Quantum Chemistry and Computing for the Curious

By Keeper L. Sharkey , Alain Chancé
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  1. Chapter 2: Postulates of Quantum Mechanics

About 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

Publication date:
May 2022



"Learning is finding out what you already know. Doing is demonstrating that you know it. Teaching is reminding others that they know just as well as you. You are all learners, doers, teachers."

– Richard Bach

Figure 0.1 – Learning quantum computing and quantum chemistry [authors]

This book aims to demystify quantum chemistry and computing, discuss the future of quantum technologies based on current limitations, demonstrate the usefulness and shortcomings of the current implementations of quantum theory, and share our love of the topic.

This book is not a traditional presentation of quantum chemistry nor quantum computing, but rather an explanation of how the two topics intertwine through the illustration of the postulates of quantum mechanics, particularly with Python code and open-source quantum chemistry packages.

Quantum chemistry has many applications in industry, from pharmaceutical design to energy creation and the development of quantum computing in recent years. With adequate knowledge of quantum chemistry and the postulates of quantum mechanics, we can overcome some of the major hurdles humanity faces and achieve positive impacts. We hope that you can learn sufficient details to be a part of the new and productive solutions moving forward.


Readers we target

All kinds of readers are welcome. However, the people who will benefit the most are those interested in chemistry and computer science at the early stages of learning; advanced high school and early college students, or professionals wanting to acquire a background in quantum chemistry as it relates to computing, both from an algorithm and hardware standpoint. We also summarize useful mathematics and calculus as it relates to solving chemistry problems. The topics will appeal to people of various industry verticals who are interested in a career in quantum computational chemistry and computing.

You will be at the forefront of exciting state-of-the-art opportunities to expand your ideas and start experimenting with your simulations.


A fast path to using quantum chemistry

We chose to write this book in such a way as to demystify the fundamentals of quantum concepts for a curious audience. This book introduces the basics of quantum chemical concepts by describing the five postulates of quantum mechanics, including how these concepts relate to quantum information theory, including basic programming examples of atomic and molecular systems with Python, SimPy [Simpy], QuTiP [QuTiP], and open-source quantum chemistry packages PySCF [PySCF], ASE [ASE_0], PyQMC [PyQMC], Psi4 [Psi4_0], and Qiskit [Qiskit] code. An introductory level of understanding Python is sufficient to read the code, and a browser is all that is required to access the Google Colaboratory and run the companion Jupyter notebooks we provide in the cloud. Each chapter includes an artistic rendering of quantum concepts related to historical quotes.

Through the 1990s, 2000s, and 2010s, there has been amazing progress in the development of computational chemistry packages and, most recently, Qiskit Nature [Qiskit_Nature] [Qiskit_Nat_0]. We outline and introduce basic quantum chemical concepts that are discussed in a modern fashion and relate these concepts to quantum information theory and computation. We use Python, PySCF, and Qiskit Nature for illustrative purposes.


Quantum chemistry

The fundamentals of quantum mechanics and the five postulates directly impact material research and computational chemistry for finding new drugs and catalysts, enabling efficient and cleaner processes for converting chemicals from one form to another. Quantum chemistry is also essential for designing future quantum computers that use the properties of atoms and/or ions. However, quantum chemistry remains an elusive topic that seemingly takes many years to master.

We think that the traditionally long-term achievement of literacy of the topic is directly related to the perceived complexity of the topic and historical approximations made to increase accessibility and usability with conventional computing. With approximation in place and wide acceptance by the scientific community as the only way forward, some fundamental concepts are often overlooked, misunderstood, and eliminated from the disciplines depending on these ideas. We see this as an opportunity to share our love of quantum chemistry in its full potential to enhance the friendliness of and approachability of the topic.

We will share sufficient details so that you understand the limitations that were historically established. For instance, we present a general formulation of the Pauli exclusion principle for all elementary particles that also holds for composite particles, which many textbooks do not adequately explain.

There is more to the quantum story but too much to be included as a first book for the curious. Therefore, we plan to write a following book that expands cutting-edge quantum ideas that are not yet widely used in the scientific community.


How to navigate the book

We advise you to follow the sequential ordering of chapters and gradually master the concepts, methods, and tools that will be useful later in the book.

  • Chapter 1, Introducing Quantum Concepts, presents a history of quantum chemistry and quantum computing, and introduces the fundamental building blocks of nature, particles and matter, light and energy, and quantum numbers.
  • Chapter 2, Postulates of Quantum Mechanics, gives a non-expert in quantum physics the concepts, definitions, and notation of quantum mechanics and quantum information theory necessary to grasp the content of this book.
  • Chapter 3, Quantum Circuit Model of Computation, introduces the quantum circuit model of computation and Qiskit Nature, an open-source framework that provides tools for computing ground state energy, excited states, and dipole moments of molecules.
  • Chapter 4, Molecular Hamiltonians, presents the molecular Hamiltonian, modeling the electronic structure of a molecule and fermions to qubit mappings.
  • Chapter 5, Variational Quantum Eigensolver (VQE) Algorithm, shows a process for solving the ground state of a molecule, focusing on the Hydrogen molecule, illustrated with the Variational Quantum Eigensolver (VQE) algorithm using Qiskit Nature.
  • Chapter 6, Beyond Born-Oppenheimer, gives a glimpse of the beyond Born-Oppenheimer approaches that have not yet been popularized.
  • Chapter 7, Conclusion, is the opening to the next book.
  • Chapter 8, References, provides a consolidated list of all the references given at the end of each chapter.
  • Chapter 9, Glossary, provides a convenient way to look up terms.
  • Appendix A, Readying Mathematical Concepts, introduces concepts with illustrations in Python code.
  • Appendix B, Leveraging Jupyter Notebooks in the Cloud, explains how to use free environments on the cloud to run the companion Jupyter notebooks we provide.
  • Appendix C, Trademarks, lists all the trademarks of the products used in this book.

To get the most out of this book

With the following software and hardware list you can access the Google Colaboratory (Colab), which is a free Jupyter Notebook environment that runs entirely in the cloud and provides online, shared instances of Jupyter notebooks without having to download or install any software:


Download the example code files

You can download the example code files for this book from GitHub at https://github.com/PacktPublishing/Quantum-Chemistry-and-Computing-for-the-Curious. If there's an update to the code, it will be updated in the GitHub repository.

To download the full version of the companion notebooks you can scan the following QR code or go to the provided link to download them.


We also have other code bundles from our rich catalog of books and videos available at https://github.com/PacktPublishing/. Check them out!


Conventions used

There are a number of text conventions used throughout this book.

Code in text: Indicates code words in text, database table names, folder names, filenames, file extensions, pathnames, dummy URLs, user input, and Twitter handles. Here is an example: "There is no loop in a quantum circuit, but we can have a classical loop that appends a quantum sub-circuit. In Qiskit we use the QuantumRegister class to create a register of qubits and the QuantumCircuit class to create a quantum circuit."

A block of code is set as follows:

q = QuantumRegister(2)
qc = QuantumCircuit(q)
qc.cx(q[0], q[1])

Any command-line input or output is written as follows:

Mo: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d⁴

Get in touch

Feedback from our readers is always welcome.

General feedback: If you have questions about any aspect of this book, email us at [email protected] and mention the book title in the subject of your message.

Errata: Although we have taken every care to ensure the accuracy of our content, mistakes do happen. If you have found a mistake in this book, we would be grateful if you would report this to us. Please visit www.packtpub.com/support/errata and fill in the form.

Piracy: If you come across any illegal copies of our works in any form on the internet, we would be grateful if you would provide us with the location address or website name. Please contact us at [email protected] with a link to the material.

If you are interested in becoming an author: If there is a topic that you have expertise in and you are interested in either writing or contributing to a book, please visit authors.packtpub.com.



[ASE_0] Atomic Simulation Environment (ASE), https://wiki.fysik.dtu.dk/ase/index.html

[NumPy] NumPy: the absolute basics for beginners, https://numpy.org/doc/stable/user/absolute_beginners.html

[Psi4_0] Psi4 manual master index, https://psicode.org/psi4manual/master/index.html

[PyQMC] PyQMC, a python module that implements real-space quantum Monte Carlo techniques, https://github.com/WagnerGroup/pyqmc

[PySCF] The Python-based Simulations of Chemistry Framework (PySCF), https://pyscf.org/

[Qiskit] Qiskit, https://qiskit.org/

[Qiskit_Nat_0] Qiskit_Nature, https://github.com/Qiskit/qiskit-nature/blob/main/README.md

[Qiskit_Nature] Introducing Qiskit Nature, Qiskit, Medium, April 6, 2021, https://medium.com/qiskit/introducing-qiskit-nature-cb9e588bb004

[QuTiP] QuTiP, Plotting on the Bloch Sphere, https://qutip.org/docs/latest/guide/guide-bloch.html

[Simpy] SimPy Discrete event simulation for Python, https://simpy.readthedocs.io/en/latest


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About the Authors

  • Keeper L. Sharkey

    Keeper L. Sharkey, PhD is the founder and CEO of ODE, L3C, a social enterprise that serves through Quantum Science, Technology and Research, qSTAR. She is Chair of Quantum Applied Chemistry at Quantum Security Alliance. She obtained a PhD in Chemical Physics from the University of Arizona as a US National Science Foundation graduate research fellow, May 2015, and a Bachelor's of Science in both Mathematics and Chemistry, May 2010. She remains a Designated Scientific Research Campus Colleague at the University of Arizona. She published over 30 manuscripts in top peer-reviewed journals regarding non-Born-Oppenheimer quantum mechanical finite-nuclear mass variational algorithms and has been cited over 400 times; H-index and i10-index of 10

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  • Alain Chancé

    Alain Chancé is Business advisor ODE, L3C and founder & CEO Quantalain SASU, a management consulting startup. He has over 30 years of experience in major enterprise transformation projects with a focus on data management and governance gained in major management consulting firms. He has a diploma ingénieur civil des Mines from École des Mines de Saint-Étienne (1981).

    Alain is co-speaker with Dr. Keeper Sharkey of the event: Next-Generation accuracy for quantum computational chemistry: introducing QLEAN™, Quantum Business Europe 2022.

    Alain is a Qiskit® Advocate and is an IBM Certified Associate Developer - Quantum Computation using Qiskit® v0.2X since 2021. He has completed a number of hackathons pertaining to quantum computing since 2018.

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Quantum Chemistry and Computing for the Curious
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