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Dancing with Qubits - Second Edition

You're reading from  Dancing with Qubits - Second Edition

Product type Book
Published in Mar 2024
Publisher Packt
ISBN-13 9781837636754
Pages 684 pages
Edition 2nd Edition
Languages
Author (1):
Robert S. Sutor Robert S. Sutor
Profile icon Robert S. Sutor

Table of Contents (26) Chapters

Preface I Foundations
Why Quantum Computing They’re Not Old, They’re Classics More Numbers Than You Can Imagine Planes and Circles and Spheres, Oh My Dimensions 6 What Do You Mean “Probably”? II Quantum Computing
One Qubit Two Qubits, Three Wiring Up the Circuits From Circuits to Algorithms Getting Physical III Advanced Topics
Considering NISQ Algorithms Introduction to Quantum Machine Learning Questions about the Future Afterword
A Quick Reference B Notices C Production Notes Other Books You May Enjoy
References
Index
Appendices

12.5 Time evolution

Another idea we need to understand for NISQ algorithms is time evolution. We begin with some results from single and multivariable calculus, complex analysis, differential equations, and linear algebra. While that is a formidable list of topics, the mathematical objects we manipulate are from Part I of this book. time evolution

Let g be a real-valued function of one real variable t. I chose t because I want you to think of it as the time variable. It is easiest to think of t having values in a continuous portion of R, although it could exclude points where g is not defined. t might take values from a finite set of numbers or a discrete set such as Z. In any case, for two values t1 and t2 in the domain of g, with t1 < t2, we can consider how g evolves when passing from t1 to t2. A common choice is t1 = 0 and t2 = 1.

For example, suppose you invest 500 units in some currency in an account that compounds interest continuously at 4% a year. Then...

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