STEM Program

Quantum Mechanics and Programming: Theory and Applications

Faculty Advisor: PhD Researcher, University of Cambridge

Program Start Time: TBD (meetings will take place for around one hour per week)

Research Program Introduction

From the foundations to the applications, how can quantum mechanics' quirky yet fundamental physics be turned into disruptive technologies? Quantum computing and related technologies promise to revolutionize fields such as pharmacology, cryptography,, and machine learning. Therefore, a worldwide research effort is focused on this technology, as the scientific and commercial rewards would be enormous.

This program introduces students to the mathematical principles of quantum mechanics and its implementation in physics. With these primitives in place, we will discuss how quantum mechanics is applied in state-of-the-art technologies. Quantum technologies are currently used for artificial intelligence, revolutionary drug discovery, financial portfolio optimization, and even art creation! We will explore these applications and everything in between.

Weekly meetings will consist of discussions of the students’ mathematical and programming exercises. Later in the program, these exercises will prepare the students to develop a programming project and technical report, the content of which will be closely linked to modern research in quantum technologies.

Final Deliverables

Students will complete a final programming project with an accompanying technical report. Depending on the nature of the project, the program should be in a high-level language such as Python or MatLab or in a high-performance language such as C++. The technical report should cover the project's theory, its efficient implementation, and results from their simulations and/or experiments. It will also discuss how these results fit into the broader field of quantum technologies.

Possible Topics For Final Project

  • Simulating a quantum computer running Shor’s algorithm from scratch in Python, C, or C++.

  • Executing Grover’s algorithm on a real/simulated quantum computer to identify objects in a small database.

  • Simulate the violation of CHSH equalities in Python.

  • Simulating photon wavefunction interference to demonstrate the Hong-Ou-Mandel effect.

  • Simulate a quantum teleportation protocol.

  • Implement supervised quantum machine learning for simple classification with a small dataset from Kaggle on a real/simulated quantum computer.

  • Simulate the BB84 quantum key distribution protocol in Python.

  • Other professor-approved topics in this subject area that you are interested in

Program Details

  • Cohort size: 3 to 5 students

  • Duration: 12 weeks

  • Workload: Around 4 to 5 hours per week (including class and homework time)

  • Target students: 9 to 12th graders interested in quantum mechanics, mathematics, theoretical physics, and/or computer science.

  • Prerequisites: Quantum mechanics is intimately tied to linear algebra. Students should understand mathematics well, particularly in vectors and matrices. Students should also learn the basics of Python.