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
Table of Contents (14 chapters)
Chapter 8: References
Chapter 9:Glossary
Appendix B: Leveraging Jupyter Notebooks on the Cloud
Appendix C: Trademarks

4.7. Fermion to qubit mappings

We consider a system of fermions, each labeled with an integer from to . We need a fermion to qubit mapping, a description of the correspondence between states of fermions and states of qubits, or, equivalently, between fermionic operators and multi-qubit operators. We need a mapping between the fermion creation and annihilation operators and multi-qubit operators. The Jordan-Wigner and the Bravyi-Kitaev transformations are widely used and simulate a system of electrons with the same number of qubits as electrons.

4.7.1. Qubit creation and annihilation operators

We define qubit operators that act on local qubits [Yepez] [Chiew], as shown in Figure 4.22:

Figure 4.22 – Qubit creation and annihilation operators

The qubit operators have the anti-commutation relation: .

4.7.2. Jordan-Wigner transformation

The Jordan-Wigner (JW) transformation stores the occupation of each spin orbital in each qubit. It maps...