Quantum Computer Programming

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.

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 Quantum machine learning algorithms

3.2 Quantum variational learning

3.3 Quantum measurement classification

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

Grades

References

• [Nielsen10] Michael A. Nielsen & Isaac L. Chuang. Quantum Computation and Quantum Information. CAMBRIDGE UNIVERSITY PRESS. 2010
• [Quiskit-TB] IBM, Qiskit Textbook
• [Asfaw19] Abraham Asfaw et al., Learn Quantum Computation using Qiskit. Qiskit Development Team. 2019 (This is the old version of the textbook and has been replaced by [Qiskit-TB], the notebooks can be accessed in this Github repository)
• [Kaye07] Phillip Kaye et al. An Introduction to Quantum Computing. Oxford University Press. 2007 9783319964232). Springer. 2018
• [Nannicini17] Nannicini, G. An introduction to quantum computing, without the physics. arXiv preprint arXiv:1708.03684. 2017
• [Rieffel11] Rieffel, E. G., & Polak, W. H. Quantum computing: A gentle introduction. MIT Press. 2011
• [Schuld18] Schuld, M., & Petruccione, F. Supervised Learning with Quantum Computers. Springer. 2018

Additional resources

• [IGFAE20] Andrés Gómez. Introduction to Quantum Computing. Short Course, Instituto Galego de Física de Altas Enerxías (IGFAE). 2020
• [CS191] Umesh Vazirani. Berkeley CS191: Qubits, Quantum Mechanics, and Computers. 2012.
• [CS269Q] Dan Boneh, Will Zeng, CS 269Q: Quantum Computer Programming, Stanford University, 2019
• [Qiskit] Qiskit: is an open source SDK for working with quantum computers at the level of pulses, circuits and algorithms. IBM.
• [IBMQE] IBM Quantum: Learn, develop, and run quantum programs.

Week	Topic	Material	Assignments
Aug 8	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)
Aug 15	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
Aug 22	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 [Qiskit-TB] Basics of quantum information: Single systems	Exercise set 2
Aug 29	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 [Qiskit-TB] Basics of quantum information: Multiple systems	Exercise set 3 Assignment 2
Sep 5	1.7 Theory of computation and Computational Complexity	Asynchronous class: Computational complexity (slides) Part 1: analysis of computational problems, how to quantify computational resources, computational complexity (video) Part 2: decision problems, P and NP, Hamiltonian and Euler cycle, problem reduction, NP-complete, complexity classes (video) Reading material: [Nielsen10] 3.2 The analysis of computational problems
Sep 12-19	2.1 Quantum circuits and gates	Asynchronous class: Single qubit gates (video) Reading material: [Qiskit-TB] Introduction to quantum computing: The atoms of computation [Qiskit-TB] Basics of quantum information: Single systems [Asfaw19] 1.3 Representing Qubit States [Asfaw19] 1.4 Single Qubit Gates	Exercise set 4
Sep 26	2.1 Quantum circuits and gates	Asynchronous class: Multiple qubit gates (video 1)(video 2)(video 3) Reading material: [Qiskit-TB] Multiple Qubits and Entangled States [Qiskit-TB] Phase Kickback [Qiskit-TB] Basic Circuit Identities	Exercise set 5 Assignment 3
Oct 3	2.2 Superdense coding and teleportation	Asynchronous class: Superdense coding and teleportation (video 1)(video 2) Reading material: [Qiskit-TB] Quantum Teleportation [Qiskit-TB] Superdense Coding	Exercise set 6
Oct 10-17	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: [Qiskit-TB] Deutsch-Jozsa Algorithm [Qiskit-TB] Simon's Algorithm
Oct 24	2.5 Quantum Fourier Transform 2.6 Quantum Phase Estimation 2.7 Shor's Algorithm 2.8 Grover's Algorithm	Reading material: [Qiskit-TB] Quantum Fourier Transform [Qiskit-TB] Quantum Phase Estimation [Qiskit-TB] Shor's Algorithm [Qiskit-TB] Grover's Algorithm
Oct 31	2.9 Quantum algorithms for applications	Reading material: [Qiskit-TB] Solving Linear Systems of Equations using HHL [Qiskit-TB] Simulating Molecules using VQE [Qiskit-TB] Solving combinatorial optimization problems using QAOA [Qiskit-TB] Solving Satisfiability Problems using Grover's Algorithm	Final Project
Nov 7	3.1 Quantum machine learning algorithms 3.2 Quantum variational learning	Quantum machine learning (slides)(video) Quantum variational learning (notebook)(video) Reading material: Pennylane introduction Crooks, G. E. (2019). Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition. arXiv preprint arXiv:1905.13311.
Nov 14	3.1 Quantum machine learning algorithms	[Qiskit-TB] Quantum Machine Learning
Nov 21	3.3 Quantum machine learning algorithms
Nov 30			Final project