Quantum Computing Book Preview

This is a preview of the book I am writing. It will cover general topics on quantum computing and some quantum physics.

This is not anywhere near the final draft so it may change.

Quantum computing has the potential to help us understand complex chemical reactions more accurately. However, simulating these reactions using a classical computer is difficult because of the large number of variables involved. In this article, we discuss some recent quantum algorithms that can estimate the phase of a chemical reaction using a plane wave basis with sublinear scaling in the number of basis functions N . The Trotter step size bound O(N log N ) for first quantized plane wave algorithms was introduced by Ryan Babbush, and is currently the best possible gate complexity bound for this setting. Recently, Low et al. showed that a quantum walk on a graph can also be implemented using plane waves with sublinear scaling in N. This algorithm has since been improved by Ian D. Kivlichan, who showed that the Trotter step size can be reduced to O(N ) without significantly compromising accuracy. While these algorithms are promising, they are not yet practical for solving real-world chemistry problems. For example, Babbush showed that the gate complexity of their first quantized plane wave algorithm scales as ̃O(η8/3N 1/3), where η is the number of electrons in the system and N is the…