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You're reading from  Quantum Computing Algorithms

Product typeBook
Published inSep 2023
PublisherPackt
ISBN-139781804617373
Edition1st Edition
Concepts
Quantum Computing
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Author (1)
Barry Burd
Barry Burd
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Barry Burd

Barry Burd received a master's degree in computer science at Rutgers University and a Ph.D. in mathematics at the University of Illinois. As a teaching assistant in Champaign–Urbana, Illinois, he was elected five times to the university-wide List of Teachers Ranked as Excellent by Their Students. Since 1980, Dr. Burd has been a professor in the department of mathematics and computer science at Drew University in Madison, New Jersey. He has spoken at conferences in the United States, Europe, Australia, and Asia. In 2020, he was honored to be named a Java Champion. Dr. Burd lives in Madison, New Jersey, USA, where he spends most of his waking hours in front of a computer screen.
Read more about Barry Burd

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Questions

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

  1. 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>&#xA0;</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>"}

  1. 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\">&#x3C0;</mi></mstyle></math>"} radians around the Z-axis. Draw the result of applying a Z gate to a |+⟩ qubit.
  2. 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.
  3. Apply the Z gate matrix from Question 3 to a |+⟩ qubit. Does the result you get confirm your answer to Question 2?
  4. Write Qiskit code to test the result you got in Questions 2, 3, and 4.
  5. 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\">&#x3C0;</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>&#xA0;</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.
  6. 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\">&#x3C0;</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>&#xA0;</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.
  7. 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\">&#x3C0;</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...
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Quantum Computing Algorithms
Published in: Sep 2023Publisher: PacktISBN-13: 9781804617373
© 2023 Packt Publishing Limited All Rights Reserved

Author (1)

author image
Barry Burd

Barry Burd received a master's degree in computer science at Rutgers University and a Ph.D. in mathematics at the University of Illinois. As a teaching assistant in Champaign–Urbana, Illinois, he was elected five times to the university-wide List of Teachers Ranked as Excellent by Their Students. Since 1980, Dr. Burd has been a professor in the department of mathematics and computer science at Drew University in Madison, New Jersey. He has spoken at conferences in the United States, Europe, Australia, and Asia. In 2020, he was honored to be named a Java Champion. Dr. Burd lives in Madison, New Jersey, USA, where he spends most of his waking hours in front of a computer screen.
Read more about Barry Burd

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