Quantum Chemistry and Computing for the Curious

Quantum Chemistry and Computing for the Curious

by Keeper L. Sharkey, Alain Chancé
Released May 2022
Publisher(s): Packt Publishing
ISBN: 9781803243900

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Book description

Acquire knowledge of quantum chemistry concepts, the postulates of quantum mechanics, and the foundations of quantum computing, and execute illustrations made with Python code, Qiskit, and open-source quantum chemistry packages

Key Features

  • Be at the forefront of a quest for increased accuracy in chemistry applications and computing
  • Get familiar with some open source quantum chemistry packages to run your own experiments
  • Develop awareness of computational chemistry problems by using postulates of quantum mechanics

Book Description

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

What you will learn

  • Understand mathematical properties of the building blocks of matter
  • Run through the principles of quantum mechanics with illustrations
  • Design quantum gate circuit computations
  • Program in open-source chemistry software packages such as Qiskit®
  • Execute state-of-the-art-chemistry calculations and simulations
  • Run companion Jupyter notebooks on the cloud with just a web browser
  • Explain standard approximations in chemical simulations

Who this book is for

Professionals interested in chemistry and computer science at the early stages of learning, or interested in a career of quantum computational chemistry and quantum computing, including advanced high school and college students. Helpful to have high school level chemistry, mathematics (algebra), and programming. An introductory level of understanding Python is sufficient to read the code presented to illustrate quantum chemistry and computing

Table of contents

  1. Quantum Chemistry and Computing for the Curious
  2. Foreword
  3. Contributors
  4. About the authors
  5. Acknowledgments
  6. About the reviewer
  7. Preface
    1. Readers we target
    2. A fast path to using quantum chemistry
    3. Quantum chemistry
    4. How to navigate the book
    5. To get the most out of this book
    6. Download the example code files
    7. Conventions used
    8. Get in touch
    9. References
    10. Share Your Thoughts
  8. Chapter 1: Introducing Quantum Concepts
    1. Technical requirements
    2. 1.1. Understanding the history of quantum chemistry and mechanics
    3. 1.2. Particles and matter
      1. Elementary particles
      2. Composite particles
    4. 1.3. Quantum numbers and quantization of matter
      1. Electrons in an atom
      2. The wave function and the PEP
    5. 1.4. Light and energy
      1. Planck constant and relation
      2. The de Broglie wavelength
      3. Heisenberg uncertainty principle
      4. Energy levels of atoms and molecules
      5. Hydrogen spectrum
      6. Rydberg constant and formula
      7. Electron configuration
      8. Schrödinger's equation
      9. Probability density plots of the wave functions of the electron in a hydrogen atom
    6. 1.5. A brief history of quantum computation
    7. 1.6. Complexity theory insights
    8. Summary
    9. Questions
      1. Answers
    10. References
  9. Chapter 2: Postulates of Quantum Mechanics
    1. Technical requirements
    2. 2.1. Postulate 1 – Wave functions
      1. 2.1.1. Spherical harmonic functions
      2. 2.1.2. Addition of momenta using CG coefficients
      3. 2.1.3. General formulation of the Pauli exclusion principle
    3. 2.2. Postulate 2 – Probability amplitude
      1. 2.2.1. Computing the radial wave functions
      2. 2.2.2. Probability amplitude for a hydrogen anion
    4. 2.3. Postulate 3 – Measurable quantities and operators
      1. 2.3.1. Hermitian operator
      2. 2.3.2. Unitary operator
      3. 2.3.3. Density matrix and mixed quantum states
      4. 2.3.4. Position operation
      5. 2.3.5. Momentum operation
      6. 2.3.6. Kinetic energy operation
      7. 2.3.7. Potential energy operation
      8. 2.3.8. Total energy operation
    5. 2.4. Postulate 4 – Time-independent stationary states
    6. 2.5. Postulate 5 – Time evolution dynamics
    7. Questions
    8. Answers
    9. References
  10. Chapter 3: Quantum Circuit Model of Computation
    1. Technical requirements
      1. Installing NumPy, Qiskit, QuTiP, and importing various modules
    2. 3.1. Qubits, entanglement, Bloch sphere, Pauli matrices
      1. 3.1.1. Qubits
      2. 3.1.2. Tensor ordering of qubits
      3. 3.1.3. Quantum entanglement
      4. 3.1.4. Bloch sphere
      5. 3.1.5. Displaying the Bloch vector corresponding to a state vector
      6. 3.1.6. Pauli matrices
    3. 3.2. Quantum gates
      1. 3.2.1. Single-qubit quantum gates
      2. 3.2.2. Two-qubit quantum gates
      3. 3.2.3. Three-qubit quantum gates
      4. 3.2.4. Serially wired gates and parallel quantum gates
      5. 3.2.5. Creation of a Bell state
      6. 3.2.6. Parallel Hadamard gates
    4. 3.3. Computation-driven interference
      1. 3.3.1. Quantum computation process
      2. 3.3.2. Simulating interferometric sensing of a quantum superposition of left- and right-handed enantiomer states
    5. 3.4. Preparing a permutation symmetric or antisymmetric state
      1. 3.4.1. Creating random states
      2. 3.4.2. Creating a quantum circuit and initializing qubits
      3. 3.4.3. Creating a circuit that swaps two qubits with a controlled swap gate
      4. 3.4.4. Post selecting the control qubit until the desired state is obtained
      5. 3.4.5. Examples of final symmetrized and antisymmetrized states
    6. References
  11. Chapter 4: Molecular Hamiltonians
    1. Technical requirements
      1. Installing NumPy, Qiskit, and importing the various modules
    2. 4.1. Born-Oppenheimer approximation
    3. 4.2. Fock space
    4. 4.3. Fermionic creation and annihilation operators
      1. 4.3.1. Fermion creation operator
      2. 4.3.2. Fermion annihilation operator
    5. 4.4. Molecular Hamiltonian in the Hartree-Fock orbitals basis
    6. 4.5. Basis sets
      1. 4.5.1. Slater-type orbitals
      2. 4.5.2. Gaussian-type orbitals
    7. 4.6. Constructing a fermionic Hamiltonian with Qiskit Nature
      1. 4.6.1. Constructing a fermionic Hamiltonian operator of the hydrogen molecule
      2. 4.6.2. Constructing a fermionic Hamiltonian operator of the lithium hydride molecule
    8. 4.7. Fermion to qubit mappings
      1. 4.7.1. Qubit creation and annihilation operators
      2. 4.7.2. Jordan-Wigner transformation
      3. 4.7.3. Parity transformation
      4. 4.7.4. Bravyi-Kitaev transformation
    9. 4.8. Constructing a qubit Hamiltonian operator with Qiskit Nature
      1. 4.8.1. Constructing a qubit Hamiltonian operator of the hydrogen molecule
      2. 4.8.2. Constructing a qubit Hamiltonian operator of the lithium hydride molecule
    10. Summary
    11. Questions
    12. References
  12. Chapter 5: Variational Quantum Eigensolver (VQE) Algorithm
    1. Technical requirements
      1. Installing NumPy, Qiskit, QuTiP, and importing various modules
    2. 5.1. Variational method
      1. 5.1.1. The Rayleigh-Ritz variational theorem
      2. 5.1.2. Variational Monte Carlo methods
      3. 5.1.3. Quantum Phase Estimation (QPE)
      4. 5.1.4. Description of the VQE algorithm
    3. 5.2. Example chemical calculations
      1. 5.2.1. Hydrogen molecule (H2)
      2. 5.2.2. Lithium hydride molecule
      3. 5.2.3. Macro molecule
    4. Summary
    5. Questions
    6. Answers
    7. References
  13. Chapter 6: Beyond Born-Oppenheimer
    1. Technical requirements
      1. Installing NumPy, SimPy, and math modules
    2. 6.1. Non-Born-Oppenheimer molecular Hamiltonian
      1. Internal Hamiltonian operator
      2. Explicitly correlated all-particle Gaussian functions
      3. Energy minimization
    3. 6.2. Vibrational frequency analysis calculations
      1. Modeling the vibrational-rotational levels of a diatomic molecule
      2. Computing all vibrational-rotational levels of a molecule
    4. 6.3. Vibrational spectra for ortho-para isomerization of hydrogen molecules
    5. Summary
    6. Questions
    7. Answers
    8. References
  14. Chapter 7: Conclusion
    1. 7.1. Quantum computing
    2. 7.2. Quantum chemistry
    3. References
  15. Chapter 8: References
  16. Chapter 9:Glossary
  17. Appendix A: Readying Mathematical Concepts
    1. Technical requirements
      1. Installing NumPy, SimPy, and Qiskit and importing various modules
    2. Notations used
    3. Mathematical definitions
      1. Pauli exclusion principle (PEP) #
      2. Angular momentum quantum number #
      3. Occupation number operator #
      4. Quantum Phase Estimation (QPE) #
      5. Complex numbers
      6. Vector space
      7. Linear operators
      8. Matrices
      9. Eigenvalues and eigenvectors
      10. Vector and matrix transpose, conjugate, and conjugate transpose
      11. Dirac's notation #
      12. Inner product of two vectors
      13. Norm of a vector
      14. Hilbert space
      15. Matrix multiplication with a vector
      16. Matrix addition
      17. Matrix multiplication
      18. Matrix inverse
      19. Tensor product
      20. Kronecker product or tensor product of matrices or vectors
      21. Kronecker sum
      22. Outer product
      23. Hermitian operator
      24. Unitary operator
      25. Density matrix #
      26. Pauli matrices
      27. Anti-commutator #
      28. Anti-commutation #
      29. Commutator
      30. Total wave function #
    4. References
  18. Appendix B: Leveraging Jupyter Notebooks on the Cloud
    1. Jupyter Notebook
      1. Google Colaboratory
      2. IBM Quantum Lab
      3. Companion Jupyter notebooks
    2. References
  19. Appendix C: Trademarks
    1. Why subscribe?
  20. Other Books You May Enjoy
    1. Packt is searching for authors like you
    2. Share Your Thoughts

Product information

  • Title: Quantum Chemistry and Computing for the Curious
  • Author(s): Keeper L. Sharkey, Alain Chancé
  • Release date: May 2022
  • Publisher(s): Packt Publishing
  • ISBN: 9781803243900