Quantum Computer Programming

2021-II

Course description

Instructor

Fabio A. González
Departamento de Ingeniería de Sistemas y Computación
Universidad Nacional de Colombia

Course goal

Quantum computing is a rapid developing field with a high potential to revolutionize the way we compute and how we use computers to solve problems. It exploits the particular nature of quantum systems to perform calculations that in some cases can exhibit exponential speed-ups with respect to classical computers. This course is an introduction to the mathematical tools necessary to describe quantum systems and the fundamental concepts of quantum circuits and algorithms. The course will provide tools that allow students to implement quantum circuits and algorithms using quantum computing libraries and to run them using quantum simulators as well as real hardware. The final part of the course will focus on the application of quantum computing to machine learning.

At the end of the course the student will be able:

  • To describe the differences between quantum and classic computation.
  • To understand the mathematical basis of quantum state representation and quantum operations.
  • To build quantum circuits connecting different types of quantum gates.
  • To implement quantum circuits and algorithms using quantum programming libraries.
  • To run quantum circuits and algorithms using quantum simulators and real quantum computers.
  • To understand how to design quantum algorithms to solve different problems.
  • To understand how to design hybrid quantum algorithms to solve machine learning problems.

Course topics

1 Quantum Computing Basis

1.1 Introduction to quantum computing

1.2 Linear algebra and Dirac notation

1.3 Qubits

1.4 Measurements

1.5 Composite systems

1.6 Pure, entangled and mixed states

1.7 Theory of computation and Computational Complexity

2 Quantum circuits and algorithms

2.1 Quantum circuits and gates

2.2 Superdense coding and teleportation

2.3 Deutsch-Joza algorithm

2.4 Simon’s algorithm

2.5 Quantum Fourier Transform

2.6 Quantum Phase Estimation

2.7 Shor’s algorithm

2.8 Grover’s algorithm

2.9 Quantum algorithms for applications

3 Quantum machine learning

3.1 Machine learning review

3.2 Quantum measurement classification

3.3 Quantum machine learning algorithms

Evaluation and grading policy

  • Participation 10%
  • Assignments 30%
  • Presentation 20%
  • Exam 20%
  • Final project 20%

Grades

Course resources

References

Additional resources

Course schedule

Week Topic Material Assignments
Oct 5-12 1.1 Introduction to quantum computing Synchronous class:
Introduction to Quantum Computing (slides)
Part 1: Past, present and future (video)
Part 2: Why quantum computing (video)
Part 3: How quantum computers work (video)
Part 4: Quantum information (video)
Part 5: How to program quantum computers (video)
Part 6: Quantum machine learning (video)
Resources : [IGFAE20] Lecture 1: Introduction to Quantum Computing (slides)
[Nielsen10] Sections 1.1 Global perspectives
Dario Gil, The Future of Quantum Computing, IBM 2020 (video)
Oct 19 1.2 Linear algebra and Dirac notation Asynchronous class:
Linear algebra review (slides)(video 1)(video 2)(video 3)
Reading material:
[Nielsen10] Section 2.1 Linear algebra
[Nielsen10] Section 2.2 Postulates of quantum mechanics
[Asfaw19] 8.1 Linear Algebra
Exercise set 1
Assignment 1
Oct 26 1.3 Qubits
1.4 Measurements
Asynchronous class:
Qubits (slides)(video 1)(video 2)
Reading material:
[CS191x] Chapter 1 Qubits and Quantum Measurement
[Nielsen10] Section 2.2 Postulates of quantum mechanics
[Asfaw19] 1. Quantum States and Qubits
Exercise set 2
Nov 2 1.5 Composite systems
1.6 Pure, entangled and mixed states 		Asynchronous class:
Entanglement (slides)(video)
Reading material:
[CS191x] Chapter 2 Entanglement
[Nielsen10] Section 2.2 Postulates of quantum mechanics
[Asfaw19] 2. Multiple Qubits and Entanglement
Exercise set 3
Assignment 2
Nov 9 1.7 Theory of computation and Computational Complexity
Asynchronous class:
Computational complexity (slides)(video)
Reading material:
[Nielsen10] 3.2 The analysis of computational problems
Nov 16 2.1 Quantum circuits and gates Asynchronous class:
Single qubit gates (video)
Reading material:
[Asfaw19] 1.2 The Atoms of Computation
[Asfaw19] 1.3 Representing Qubit States
[Asfaw19] 1.4 Single Qubit Gates
 Exercise set 4
Nov 23-30 2.1 Quantum circuits and gates Asynchronous class:
Multiple qubit gates (video 1)(video 2)(video 3)
Reading material:
[Asfaw19] 2.2 Multiple Qubits and Entangled States
[Asfaw19] 2.3 Phase Kickback
[Asfaw19] 2.4 More Circuit Identities
 Exercise set 5
Assignment 3
Dec 7 2.2 Superdense coding and teleportation Asynchronous class:
Superdense coding and teleportation (video 1)(video 2)
Reading material:
[Asfaw19] 3.10 Quantum Teleportation
[Asfaw19] 3.11 Superdense Coding
Dec 14 2.3 Deutsch-Joza algorithm
2.4 Simon's algorithm 		Asynchronous class:
Deutsch-Joza algorithm (slides)(video 1)
Simon's algorithm (slides)(video 1, video 2)
Reading material:
[Asfaw19] 3.2 Deutsch-Jozsa Algorithm
[Asfaw19] 3.4 Simon's Algorithm
Jan 11 2.5 Quantum Fourier Transform
2.6 Quantum Phase Estimation
2.7 Shor's Algorithm
2.8 Grover's Algorithm
Reading material:
[Asfaw19] 3.5 Quantum Fourier Transform
[Asfaw19] 3.6 Quantum Phase Estimation
[Asfaw19] 3.7 Shor's Algorithm
[Asfaw19] 3.8 Grover's Algorithm
 Final Project
Jan 18 2.9 Quantum algorithms for applications Reading material:
[Asfaw19] 4.1.1 Solving Linear Systems of Equations using HHL
[Asfaw19] 4.1.2 Simulating Molecules using VQE
[Asfaw19] 4.1.3 Solving combinatorial optimization problems using QAOA
[Asfaw19] 4.1.4 Solving Satisfiability Problems using Grover's Algorithm
Jan 25 3.1 Machine learning review
3.2 Quantum measurement classification
Feb 1 3.3 Quantum machine learning algorithms

Final Projects