Quantum Chemistry and Computing for the Curious: Illustrated with Python and Qiskit® code
- Length: 354 pages
- Edition: 1
- Language: English
- Publisher: Packt Publishing
- Publication Date: 2022-05-20
- ISBN-10: 1803243902
- ISBN-13: 9781803243900
- Sales Rank: #1006422 (See Top 100 Books)
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
Quantum Chemistry and Computing for the Curious Foreword Contributors About the authors Acknowledgments About the reviewer 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 Chapter 1: Introducing Quantum Concepts Technical requirements 1.1. Understanding the history of quantum chemistry and mechanics 1.2. Particles and matter Elementary particles Composite particles 1.3. Quantum numbers and quantization of matter Electrons in an atom The wave function and the PEP 1.4. Light and energy Planck constant and relation The de Broglie wavelength Heisenberg uncertainty principle Energy levels of atoms and molecules Hydrogen spectrum Rydberg constant and formula Electron configuration Schrödinger's equation Probability density plots of the wave functions of the electron in a hydrogen atom 1.5. A brief history of quantum computation 1.6. Complexity theory insights Summary Questions Answers References Chapter 2: Postulates of Quantum Mechanics Technical requirements 2.1. Postulate 1 – Wave functions 2.1.1. Spherical harmonic functions 2.1.2. Addition of momenta using CG coefficients 2.1.3. General formulation of the Pauli exclusion principle 2.2. Postulate 2 – Probability amplitude 2.2.1. Computing the radial wave functions 2.2.2. Probability amplitude for a hydrogen anion 2.3. Postulate 3 – Measurable quantities and operators 2.3.1. Hermitian operator 2.3.2. Unitary operator 2.3.3. Density matrix and mixed quantum states 2.3.4. Position operation 2.3.5. Momentum operation 2.3.6. Kinetic energy operation 2.3.7. Potential energy operation 2.3.8. Total energy operation 2.4. Postulate 4 – Time-independent stationary states 2.5. Postulate 5 – Time evolution dynamics Questions Answers References Chapter 3: Quantum Circuit Model of Computation Technical requirements Installing NumPy, Qiskit, QuTiP, and importing various modules 3.1. Qubits, entanglement, Bloch sphere, Pauli matrices 3.1.1. Qubits 3.1.2. Tensor ordering of qubits 3.1.3. Quantum entanglement 3.1.4. Bloch sphere 3.1.5. Displaying the Bloch vector corresponding to a state vector 3.1.6. Pauli matrices 3.2. Quantum gates 3.2.1. Single-qubit quantum gates 3.2.2. Two-qubit quantum gates 3.2.3. Three-qubit quantum gates 3.2.4. Serially wired gates and parallel quantum gates 3.2.5. Creation of a Bell state 3.2.6. Parallel Hadamard gates 3.3. Computation-driven interference 3.3.1. Quantum computation process 3.3.2. Simulating interferometric sensing of a quantum superposition of left- and right-handed enantiomer states 3.4. Preparing a permutation symmetric or antisymmetric state 3.4.1. Creating random states 3.4.2. Creating a quantum circuit and initializing qubits 3.4.3. Creating a circuit that swaps two qubits with a controlled swap gate 3.4.4. Post selecting the control qubit until the desired state is obtained 3.4.5. Examples of final symmetrized and antisymmetrized states References Chapter 4: Molecular Hamiltonians Technical requirements Installing NumPy, Qiskit, and importing the various modules 4.1. Born-Oppenheimer approximation 4.2. Fock space 4.3. Fermionic creation and annihilation operators 4.3.1. Fermion creation operator 4.3.2. Fermion annihilation operator 4.4. Molecular Hamiltonian in the Hartree-Fock orbitals basis 4.5. Basis sets 4.5.1. Slater-type orbitals 4.5.2. Gaussian-type orbitals 4.6. Constructing a fermionic Hamiltonian with Qiskit Nature 4.6.1. Constructing a fermionic Hamiltonian operator of the hydrogen molecule 4.6.2. Constructing a fermionic Hamiltonian operator of the lithium hydride molecule 4.7. Fermion to qubit mappings 4.7.1. Qubit creation and annihilation operators 4.7.2. Jordan-Wigner transformation 4.7.3. Parity transformation 4.7.4. Bravyi-Kitaev transformation 4.8. Constructing a qubit Hamiltonian operator with Qiskit Nature 4.8.1. Constructing a qubit Hamiltonian operator of the hydrogen molecule 4.8.2. Constructing a qubit Hamiltonian operator of the lithium hydride molecule Summary Questions References Chapter 5: Variational Quantum Eigensolver (VQE) Algorithm Technical requirements Installing NumPy, Qiskit, QuTiP, and importing various modules 5.1. Variational method 5.1.1. The Rayleigh-Ritz variational theorem 5.1.2. Variational Monte Carlo methods 5.1.3. Quantum Phase Estimation (QPE) 5.1.4. Description of the VQE algorithm 5.2. Example chemical calculations 5.2.1. Hydrogen molecule (H2) 5.2.2. Lithium hydride molecule 5.2.3. Macro molecule Summary Questions Answers References Chapter 6: Beyond Born-Oppenheimer Technical requirements Installing NumPy, SimPy, and math modules 6.1. Non-Born-Oppenheimer molecular Hamiltonian Internal Hamiltonian operator Explicitly correlated all-particle Gaussian functions Energy minimization 6.2. Vibrational frequency analysis calculations Modeling the vibrational-rotational levels of a diatomic molecule Computing all vibrational-rotational levels of a molecule 6.3. Vibrational spectra for ortho-para isomerization of hydrogen molecules Summary Questions Answers References Chapter 7: Conclusion 7.1. Quantum computing 7.2. Quantum chemistry References Chapter 8: References Chapter 9:Glossary Appendix A: Readying Mathematical Concepts Technical requirements Installing NumPy, SimPy, and Qiskit and importing various modules Notations used Mathematical definitions Pauli exclusion principle (PEP) # Angular momentum quantum number # Occupation number operator # Quantum Phase Estimation (QPE) # Complex numbers Vector space Linear operators Matrices Eigenvalues and eigenvectors Vector and matrix transpose, conjugate, and conjugate transpose Dirac's notation # Inner product of two vectors Norm of a vector Hilbert space Matrix multiplication with a vector Matrix addition Matrix multiplication Matrix inverse Tensor product Kronecker product or tensor product of matrices or vectors Kronecker sum Outer product Hermitian operator Unitary operator Density matrix # Pauli matrices Anti-commutator # Anti-commutation # Commutator Total wave function # References Appendix B: Leveraging Jupyter Notebooks on the Cloud Jupyter Notebook Google Colaboratory IBM Quantum Lab Companion Jupyter notebooks References Appendix C: Trademarks Why subscribe? 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