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

3.2. Quantum gates

Quantum gates are unitary operators () working on one, two, or three qubits. The norm is preserved when applied to a quantum state. The action of a quantum gate on a quantum state corresponds to the multiplication of the matrix representing the gate by the vector representing the quantum state: .

In this section, a tensor product of qubits is represented with the first qubit on the left-most side of the tensor product: where . Please note that we are not using the Qiskit tensor ordering of qubits unless specifically specified.

In this section, we cover the following:

  • Section 3.2.1, Single-qubit quantum gates
  • Section 3.2.2, Two-qubit quantum gates
  • Section 3.2.3, Three-qubit quantum gates
  • Section 3.2.4, Serial wired gates and parallel quantum gates
  • Section 3.2.5, Creation of a Bell state
  • Section 3.2.6, Parallel Hadamard gates

3.2.1. Single-qubit quantum gates

A single-qubit gate has a unitary matrix form: .

In this...