You're reading from Quantum Computing Algorithms

Product type Book

Published in Sep 2023

Publisher Packt

ISBN-13 9781804617373

Pages 342 pages

Edition 1st Edition

Languages

Concepts

Quantum Computing

Author (1):

Barry Burd

Table of Contents (19) Chapters

Preface

Introduction to Quantum Computing

Part 1 Nuts and Bolts

Chapter 1: New Ways to Think about Bits

Chapter 2: What Is a Qubit?

Chapter 3: Math for Qubits and Quantum Gates

Chapter 4: Qubit Conspiracy Theories

Part 2 Making Qubits Work for You

Chapter 5: A Fanciful Tale about Cryptography

Chapter 6: Quantum Networking and Teleportation

Part 3 Quantum Computing Algorithms

Chapter 7: Deutsch’s Algorithm

Chapter 8: Grover’s Algorithm

Chapter 9: Shor’s Algorithm

Part 4 Beyond Gate-Based Quantum Computing

Chapter 10: Some Other Directions for Quantum Computing

Assessments

Index

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Questions

Answer the following questions to test your knowledge of this chapter:

Which of the following vectors represents a qubit state?

A. ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfrac><mn>1</mn><msqrt><mn>7</mn></msqrt></mfrac><mo> </mo><mfenced><mtable><mtr><mtd><msqrt><mn>3</mn></msqrt></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mstyle></math>"}$

B. ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mstyle></math>"}$

C. ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mstyle></math>"}$

In quantum computing, the Z gate rotates a Bloch sphere ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mi mathvariant=\"normal\">π</mi></mstyle></math>"}$ radians around the Z-axis. Draw the result of applying a Z gate to a |+⟩ qubit.
The matrix representation of a Z gate is ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mstyle></math>"}$ . Check to make sure that this matrix is unitary.
Apply the Z gate matrix from Question 3 to a |+⟩ qubit. Does the result you get confirm your answer to Question 2?
Write Qiskit code to test the result you got in Questions 2, 3, and 4.
The matrix representation of ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><msub><mi>R</mi><mi>Y</mi></msub><mfenced><mfrac><mi mathvariant=\"normal\">π</mi><mn>2</mn></mfrac></mfenced></mstyle></math>"}$ is ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mo> </mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mstyle></math>"}$ . Check to make sure that this matrix is unitary.
Verify that the matrix representation of ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><msub><mi>R</mi><mi>Y</mi></msub><mfenced><mfrac><mi mathvariant=\"normal\">π</mi><mn>2</mn></mfrac></mfenced></mstyle></math>"}$ is ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mo> </mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></mstyle></math>"}$ . Use the last formula in this chapter’s Experimenting with rotations section.
In Step 2 of the Experimenting with rotations section, applying ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><msub><mi>R</mi><mi>Y</mi></msub><mfenced><mfrac><mi mathvariant=\"normal\">π</mi><mn>2</mn></mfrac></mfenced></mstyle></math>"}$ to |0⟩ has the same effect as applying ${"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mi>H</mi></mstyle></math>"}$ to |0⟩. Do the matrix calculation...