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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

7.2 Bras and kets

It’s now time to formalize our understanding of |0⟩ and |1⟩ and relate them to the discussion of linear algebra in Chapter 5, “Dimensions.”

When we previously looked at vector notation in section 5.4.2, we saw several forms, such as bra ket vector$bra vector$ket Dirac, Paul Dirac bra-ket notation ⟨ | (bra) | ⟩ (ket)

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We now add two more invented by Paul Dirac, an English theoretical physicist, for use in quantum mechanics. They simplify many of the expressions we use in quantum computing.

Given a vector v = (v1, v2, …, vn), we denote by v|, pronounced “bra-v,” the row vector

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where we take the complex conjugate of each entry.

For w = (w1, w2, …, wm), |w, pronounced “ket-w,” is the column vector

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without the conjugations.

To avoid notational overload, I continue to put vector...

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