PHY 299-02 Syllabus (Tentative)

Introduction to Quantum Computing and Information

Course Introduction

This course is a 16 week introduction to quantum computing with applications in business, finance, communications, science, and engineering. There is no expected background for this course but prior experience with linear algebra, quantum mechanics, and Python programming will make the first weeks of the course easier. This course will consist of 12 weeks of lectures introducing the main concepts in quantum computing as well as cutting edge applications to machine learning, finance, and science. Quantum computing codes will be run on both simulated quantum computers and real quantum computers. The remaining 4 weeks of this course are devoted to creating and presenting a final project on a topic of your choice.  Homeworks will be given weekly during the first 12 weeks of the course and the final project will make up the other half of the course's grade.

Learning Goals

1. Be able to define the term quantum computing and explain the differences between a quantum computer and a classical computer

2.  Be able to understand the physics, mathematics, and programming background necessary to learn quantum computing

3. Be able to explain the basic principles behind quantum computers including qubits, superposition, measurement, and entanglement

4.  Be able to use a variety of quantum gates to construct quantum circuits

5. Be able to explain and implement basic quantum algorithms including quantum parallelism, Deutch-Jozsa algorithm, and Grover's search algorithm

6. Be able to explain how quantum computers can be used for communication and cryptography and be able to implement a quantum teleport protocol

7. Be able to explain and implement the variational quantum eigensolver to find eigenvalues and to find the ground state energy of a quantum system

8. Be able to explain how hybrid classical-quantum algorithm are implemented and in what types of problems they are useful

9. Be able to explain how quantum computer hardware works and its scalability 

10. Be able to explain the sources of quantum error and noise and how they can be corrected

11. Be able to explain how quantum computers can be used for machine learning, finance, and science

Textbooks and Other Resources

WARNING: IBM has recently updated their interfaces and the Qiskit library so many "older" resources you find online (i.e. older than a year) likely have out-of-date syntax. You can still use any ideas you get from those sources, but you will have to update the code.

• Quantum Computing for Programmers by Robert Hundt

• Avaliable for free on the Mount Union internet

• Quantum Computing and Quantum Information by Issac Chaung and Michael Nielsen

• Q is for Quantum by Terry Rudolph

• Available for free in three PDF files

• Python 3 programming language, Jupyter notebooks, and the libraries numpy, scipy, matplotlib, and qiskit

Grading

• 50% of the final grade will come from homework. There are 12 homeworks in total and the lowest two scores will be dropped

• 50% of the final grade will come from the final project. This will be split up as follows: implementation (20%), report (20%), and presentation (10%)

Final Project Guidelines

This course will culminate in a final project where you will complete one of the projects listed in the next section and report your results and findings both in a written report (due the last day of the course) and in a 10 minute presentation (to take place during the last week of the course).

Final Project Topics

• Create a quantum version of a simple classic game such as tic-tac-toe

• Calculate the ground state energy of simple molecular or nuclear systems using the variational quantum eigensolver and compare to the energies found with classical methods and/or analytical solutions

• Simulate a quantum key distribution for quantum cryptography

• Develop a simple quantum neural network and compare its performance to a classical neural network on simple data sets

• Develop a quantum random number generator and compare to classical random number generators

• Experiment with various ways to optimize quantum circuits

• Explore the quantum Fourier transform algorithm and its applications (ex: Shor's algorithm and large number factorization)

• Implement a hybrid classical-quantum optimization algorithm and compare to a purely classical implementation of the same algorithm

Lectures

Week 1

• Monday: What are quantum computers? How do quantum computers compare to classical computers?

• Wednesday: Linear Algebra Overview; Using Python and Numpy for Linear Algebra

• Friday: Quantum Mechanics Crash Course Part 1 (Probability, Superposition, Quantum States, Hamiltonians, Bra-Ket Notation)

Week 2

• Monday: No Class

• Wednesday: Quantum Mechanics Crash Course Part 2 (Pauli Matrices and Other Operators, Variational Principle)

• Friday: Solving Quantum Mechanics Problems in Python

Week 3

• Monday: Qubits, Superposition, and Introduction to Qiskit

• Wednesday: Quantum Measurement and Wavefunction Collapse

• Friday: Quantum Entanglement

Week 4

• Monday: Quantum Gates 

• Wednesday: Quantum Gates

• Friday: Quantum Circuits

Week 5

• Monday: Quantum Circuits

• Wednesday: Quantum Circuits

• Friday: Quantum Parallelism

Week 6

• Monday: Quantum Parallelism

• Wednesday: Deutsch-Jozsa Algorithm

• Friday: Deutsch-Jozsa Algorithm

Week 7

• Monday: Grover's Search Algorithm

• Wednesday: Grover's Search Algorithm

• Friday: Quantum Key Distribution

Week 8

• Monday: Quantum Teleportation

• Wednesday: Quantum Cryptography

• Friday: No Class

Week 9

• Monday: Quantum Simulations of Physical Systems

• Wednesday: Variational Quantum Eigensolver (VQE)

• Friday: Variational Quantum Eigensolver (VQE)

Week 10

• Monday: Variational Quantum Eigensolver (VQE)

• Wednesday: Hybrid Quantum-Classical Algorithms

• Friday: Hybrid Quantum-Classical Algorithms

Week 11

• Monday: Quantum Errors and Noise

• Wednesday: Quantum Error Correction

• Friday: Quantum Error Correction; Introduction to Final Projects

Week 12

• Monday: Quantum Hardware

• Wednesday: Quantum Hardware

• Friday: Scalability of Quantum Computers

Week 13

• Monday: An Overview of Quantum Machine Learning

• Wednesday: An Overview of Quantum Computing for Finance

• Friday: An Overview of Quantum Computing for Science and Engineering

Week 14

• Monday: Using Real Quantum Computers

• Wednesday: Using Real Quantum Computers

• Friday: Work on Final Projects in Class

Week 15

• Monday: Work on Final Projects in Class

• Wednesday: Work on Final Projects in Class

• Friday: Work on Final Projects in Class

Week 16

• Monday: Presentations on Final Projects

• Wednesday: Presentations on Final Projects

• Friday: No Class

Homeworks (Assigned on Monday, Due the Following Wednesday)

• Week 1: Linear Algebra and Quantum Mechanics Crash Course

• Week 2: Quantum Mechanics with Python

• Week 3: Simulating Qubits, Superposition, Entanglement, and Measurement with Qiskit

• Week 4: Simulating Quantum Gates and Circuits; Creating a Bell State and Demonstrating Entanglement

• Week 5: Simulating More Complicated Quantum Circuits

• Week 6: Implementing and Testing Deutsch-Jozsa Algorithm

• Week 7: Implementing Grover's Search Algorithm and Comparing to Classical Search Algorithms

• Week 8: Implementing a Quantum Teleport Protocol

• Week 9: Solving the Lipkin Model with the Variational Quantum Eigensolver

• Week 10: Solving the Lipkin Model with the Variational Quantum Eigensolver (Continued)

• Week 11: Simulating Error Propagation and Error Correction in a Noisy Quantum Circuit

• Week 12: Performing Calculations on Real Quantum Computers

• Week 13: Work on Final Projects

• Week 14: Work on Final Projects

• Week 15: Work on Final Projects