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Dancing with Qubits

Dancing with Qubits

By : Robert S. Sutor
5 (24)
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Dancing with Qubits

Dancing with Qubits

5 (24)
By: Robert S. Sutor

Overview of this book

Dancing with Qubits, Second Edition, is a comprehensive quantum computing textbook that starts with an overview of why quantum computing is so different from classical computing and describes several industry use cases where it can have a major impact. A full description of classical computing and the mathematical underpinnings of quantum computing follows, helping you better understand concepts such as superposition, entanglement, and interference. Next up are circuits and algorithms, both basic and sophisticated, as well as a survey of the physics and engineering ideas behind how quantum computing hardware is built. Finally, the book looks to the future and gives you guidance on understanding how further developments may affect you. This new edition is updated throughout with more than 100 new exercises and includes new chapters on NISQ algorithms and quantum machine learning. Understanding quantum computing requires a lot of math, and this book doesn't shy away from the necessary math concepts you'll need. Each topic is explained thoroughly and with helpful examples, leaving you with a solid foundation of knowledge in quantum computing that will help you pursue and leverage quantum-led technologies.
Table of Contents (26 chapters)
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1
I Foundations
8
II Quantum Computing
14
III Advanced Topics
18
Afterword
22
Other Books You May Enjoy
23
References
24
Index
Appendices

7.7 Gates and unitary matrices

The collection of all 2-by-2 unitary matrices (section 5.8) with entries in C form a group under multiplication called the unitary group of degree 2. We denote it by U(2, C). It is a subgroup of GL(2, C), the general linear group of degree 2 over C.

Every 1-qubit gate corresponds to such a unitary matrix. We can create all 2-by-2 unitary matrices from the identity and Pauli matrices. Pauli$matrix matrix$Pauli operator$Pauli

We can write any U(2, C) as a product of a complex unit times a linear combination of unitary matrices

Displayed math

with

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where we have the following definitions, properties, and identities:

  • 0 ≤ θ < 2π
  • cI2 is in R
  • cσx, cσy, and cσz are in C
  • |cI2|2 + |cσx|2 + |cσy|2 + |cσz|2 = 1

and

Displayed math

The complex unit only affects the global phase of the qubit state and so...

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