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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

12.8 Quantum approximate optimization algorithm (QAOA)

The quantum approximate optimization algorithm, abbreviated as QAOA, is an example of a variational quantum algorithm. We can use it for combinatorial optimization problems such as the Max-Cut Problem we discussed in section 12.2.2, and we use this problem to illustrate the technique. 18 38 algorithm$QAOA algorithm$quantum approximate optimization quantum$approximate optimization algorithm algorithm$variational QAOA variational$algorithm Max-Cut Problem algorithm$QAOA maximum cut

We begin by constructing the Hamiltonians, unitaries, and circuits we need to perform the optimization.

12.8.1 Encoding the problem

Recall from section 12.2.2 on the Max-Cut Problem that we use the integer vector z with zk = ±1. zk = 1 if k is in U, and zk = –1 if k is in U. We seek to maximize

Displayed math

We now map this general form with n vertices to Hermitian Pauli strings and a...

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