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Fundamentals of Quantum Algorithms
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Welcome to Fundamentals of Quantum Algorithms, the second course in the Understanding Quantum Information and Computation series comprising the following courses:

This course explores computational advantages of quantum information, including what we can do with quantum computers and their advantages over classical computers. It begins with quantum query algorithms, which offer simple proof of concept demonstrations for quantum algorithms, and then moves on to quantum algorithms for problems including integer factorization and unstructured search.

This course is intended for students, professionals, and hobbyists in fields such as computer science, physics, engineering, and mathematics who are eager to gain knowledge on the theoretical foundations of quantum information and computation.

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Lessons

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Quantum query algorithms
  • Introduction
  • Pre-course Survey
  • The query model of computation
  • Deutsch's algorithm
  • The Deutsch-Jozsa algorithm
  • Simon's algorithm
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Quantum algorithmic foundations
  • Introduction
  • Two examples: factoring and GCDs
  • Measuring computational cost
  • Classical computations on quantum computers
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Phase-estimation and factoring
  • Introduction
  • The phase estimation problem
  • Phase estimation procedure
  • Shor's algorithm
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Grover's algorithm
  • Introduction
  • Unstructured search
  • Grover's algorithm
  • Analysis
  • Choosing the number of iterations
  • Qiskit implementation
  • Concluding remarks
  • Post-Course Survey
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Exam

Take this exam to test your skills. This exam is intended to be taken after reading the lessons in this course. Once you have completed the exam, come back here to see your earned badge.

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Helpful materials

Learning goals

Upon completing the course, you will be able to:

  • Evaluate the behavior of quantum algorithms, including Deutsch's algorithm, the Deutsch–Jozsa algorithm, Simon's algorithm, and Grover's algorithm, on specific problem instances.
  • Analyze quantum circuits based on the quantum phase estimation technique.
  • Implement basic query algorithms, phase estimation, and Grover's algorithm using Qiskit.
  • Compare the computational costs of quantum algorithms and classical algorithms for selected problems.

Additional references

Alongside this course, you may find these resources to be helpful or interesting:

Presentation slides

Copies of the slides used to create the videos for this course are available for download in pdf format.