Immersion Workshop: Introduction to Quantum Computing

Presenters of the Immersions workshop: David Hoe and Mary Lowe

We are planning to offer three different Immersions from 2026 to 2028. For Summer 2026, the goal is for each participant to develop a curriculum plan for teaching undergraduate introductory quantum computing (QC). The following is a summary of topics in our Introduction to QC course at Loyola University Maryland. Our course is a combination of lecture and active learning exercises using paper-and-pencil and/or computer. If you feel that our instructional materials would be useful for the implementation of QC at your institution, please consider attending this workshop. We are happy to share our lectures, active learning materials, and homework problems with solutions, and can follow up with you as you implement QC curriculum materials at your institution. We have NSF funding to cover travel costs.

Participants are welcome from physics, engineering, computer science, math, chemistry, or related areas. No prior knowledge of quantum mechanics, quantum computing, or physics is necessary. 

We will be running the course again in Spring 2026 and will update this summary as further improvements are made. 

Course logistics at Loyola

• Schedule: Tuesday and Thursday 1:40 – 2:55 pm + homework + in-class exams
• Classes: In-person, lecture, active-learning exercises
• Pre-reqs: Introduction to programming course, Calculus I
• Students: Mostly undergraduates majoring in EE, CS, PH

Types of active learning in our course

• Short exercises: these are interspersed throughout all of the lectures. Students are asked to work with their neighbor. Think-pair-share. 
• Medium exercises:  students are placed in groups. 15-30 min problems.
• Flipped classroom combined with medium exercises (e.g., intro to matrices, trig review).
• Medium computer exercises using Python. See Computer Activities below.
• Short-medium exercises:
  
  • Homework problems with solutions that can also be used in class
  • We will also be incorporating materials from Adaptable Curricular Exercises for QIS by Passante, Wilcox, Pollock and Corsiglia
• Long exercises, e.g., interactive team-based activities called "Jigsaws."

Course Overview

Introduction

1. PPT slides: Timeline of QC; role of EE, CS, PH; QC interface electronics; end of Moore's law; quantum stack and need for "quantum-aware" engineers and CS
2. Quantum hardware (e.g., trapped ions and superconducting qubits); noise introduction (NISQ)
3. Classical logic gates, worksheet
4. What is a qubit, what is a stationary state
5. Classical bit versus quantum bit: ways of illustrating the difference especially for visual learners
6. Complex numbers

Single Qubits

1. Dirac notation (bra-ket), gates as operators, focus initially on kets so students can get used to them
2. Bloch Sphere and two state-system - Jigsaw
3. Inner Products, normalization
4. Superposition, interference
5. Unitary, reversible gates
6. Quantum measurement – paper-and-pencil exercises, Python exercise
7. Qubits as column vectors, gates as matrices
8. No-cloning theorem
9. Quantum circuit diagrams

Two-Qubits

1. State space
2. Tensor Products
3. Two qubit gates
   
   1. CNOT worksheet on matrix
   2. Universal gate set
4. Entanglement 
5. Quantum circuit diagrams

Multi-qubits and quantum circuits

1. Three qubit gates (e.g., Toffoli Gate, Fredkin Gate)
2. Quantum teleportation
3. Superdense coding – in HW
4. Controlled-U, swap gates
5. Outer product representation of multiqubit matrices - Jigsaw

Quantum Algorithms

1. Quantum adder
   1. Lecture showing logic, groupings to form gates
   2. Jigsaw
   3. Quirk or Circuit Composer exercise
2. Deutsch’s algorithm
   1. Jigsaw, paper-and-pencil exercises, Python exercise
3. Grover’s search algorithm
   1. Overview – lecture
   2. Quantum parallelism/superposition, n-qubits, class exercise
   3. Geometrical Interpretation, significance of iterations, paper-and-pencil exercise
   4. Amplitude amplification - Python exercise
   5. Oracle
   6. Diffusion operator with gates
4. Deutsch-Jozsa algorithm
   
   1. Overview, n-qubits, lecture; Quirk or IBM Circuit Composer exercise
   2. n = 2 case, lecture, class exercises
   3. General n-qubit case and compact notation

Computer activities

1. Set up computer – class exercise
2. Basic Python with Numpy library – class exercise
3. Numpy arrays targeted at QC – class exercise
4. Graphical platforms (IBM Circuit Composer, Quirk)
5. Quantum circuit simulators (Qiskit or Pennylane)
6. Activities embedded in the above topics

Class research projects

1. A few examples that can be done over ~3 weeks
   1. Improving the simulation of quantum computers using parallel computation
   2. Implementing advanced adder designs on a quantum computer
   3. Simple data classifier using a Hadamard gate: a study in quantum machine learning

Math concepts

1. Trig review 
2. Unit vectors (as basis vectors). Preparation for kets.
3. Introduction to matrices (student refers to web resources, e.g., How to Multiply Matrices)
4. Complex numbers
5. Linear algebra: matrix operations and bra-ket operations