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Introduction
One of the main goals of the Quantum+Chips summer school is to get the students familiarized with implementing physical problems through computer programming. To this end, every lecture day will be accompanied by a computer lab where the students will go through demonstrations of computer implementations of the material discussed in lecture that day.
There are many ways to solve physical problems with the help of a computer. In Quantum+Chips, we will use the Python programming language which is widely used not just for educational but also for advanced research purposes, making it a very suitable platform for our goals. Python can be installed in the most used operating systems and it can be used through the terminal or an user interface, such as VS Code. Here is a guide on how to install Python and VS Code on your local machine. In case you prefer, you can use other platforms such as installing Jupyter notebook in your local computer or using Google colabs.
Lead Coordinator: Johnathas D. S. Forte (sever741 at umn dot edu).
Computer Labs & Hackaton
Each day of the first week will cover a different topic. By the end, the students will participate in a Hackaton where they come up with a computer project based on the presented material. The project will be graded and the winning team will be awarded. More details on this to come.
1. Quantum Physics Day
Instructor: Johnathas D. S. Forte
On this day, students will learn basic concepts of the quantum theory. The computer lab will have examples such as the propagation of a Gaussian wavepacket through a double slit. Here is a description of the problem and here you can find the Jupyter notebook for that. Here are the slides used during Day 1.The output of the provided code is the following GIF file:
Gaussian wavepacket propagation through a double slit. Animated visualization of a two-dimensional Gaussian wavepacket propagating in the xxx-direction toward a vertical double-slit potential. As the wavepacket reaches the slits, it undergoes diffraction, forming characteristic interference patterns in the region beyond the slits. The simulation illustrates key features of quantum coherence and wave behavior, highlighting how the slits modulate the spatial evolution of the probability density.
2. Semiconductor Day
Instructor: Seungjun Lee
On this day, students will learn basic concepts of the electronic structure of crystal solid and the tight-binding method. The computer lab will have examples of tight-binding calculations including the electronic structure of a 1D atomic chain and silicon. Here is a description of the problem and here you can find the Jupyter notebook for that. The slides used in the instruction for Day 2 can be found here. The output of the provided code shows the electronic structures of silicon, presented in the following image:
Silicon band structure using the Tight-Binding model. Comparison of silicon's electronic band structure computed using the tight-binding method with varying interaction ranges. The first frame includes nearest-neighbor and one next-nearest-neighbor (NNN) couplings, resulting in a direct bandgap at the Γ point. The second frame includes interactions up to third-nearest neighbors, revealing an indirect bandgap between Γ and a point away from it, reflecting the increased accuracy in reproducing silicon's known band characteristics. .
3. Spintronics Day
Instructor: Duarte J. P. Sousa
On this day, students will learn basic concepts of spintronics dynamics. The computer lab will have examples of solving the Landau-Lifshitz-Gilbert equation. Here is a description of the problem and here you can find the Jupyter notebook for the computer lab. The output of the provided code shows the magnetization dynamic:
Magnetization dynamics. Time evolution of the magnetization vector, obtained by numerically solving the Landau–Lifshitz–Gilbert (LLG) equation. The figure on the left side shows a stable magnetic precession around the z axis while the figure on the right side hows a full magnetization switching, which is achieved whtn the current crosses over a critical value.
4. Quantum Computing Days I and II
Instructors: Johnathas D. S. Forte and Sami Farrag
On these days, the students will learn basic concepts of quantum computing, including the basic single and two-qubit gates, entanglement. The students will also learn some deeper concepts such as the CHSH Inequality and an applied physics example - the Jaynes-Cummings Hamiltonian, with the code available here. For the CHSH inequality example, click here and here for the python programs and here for the description of the problem.
Cavity QED. Time-dependent expectation values of the cavity photon number and atomic excitation probability in a quantum electrodynamics (QED) cavity, modeled using the Jaynes–Cummings Hamiltonian. The first frame shows coherent Rabi oscillations in the absence of dissipation, demonstrating idealized energy exchange between the atom and the cavity mode. In the second frame, decay processes are included, leading to damping of oscillations and energy leakage from the system, which illustrates the role of decoherence in realistic cavity-QED dynamics.
CHSH Inequality. Violation of the CHSH inequality as a function of the entanglement angle ϕ. The CHSH value is computed for the two-qubit entangled Bell pair parametrized by the entanglement angle. The curve exceeds the classical bound of 2 (dashed line) and reaches the maximum quantum limit of 2 times square root of 2, demonstrating the dependence of nonlocal correlations on the degree of entanglement.
Projects & Grading
Based on the material taught during the first week, the students will be divided into groups of 2-4 members and develop a project that will be submitted by August 6 (Wednesday, second week) at 5pm. The projects shall follow the same structure as the material posted above:
A LaTeX document following the provided template.
Submission of code with a deliverable plot or animation.
Grading will be broken down into four parts:
Working Python code
Code runs without errors
Evaluation of the 2 page paper
Clarity of the explanation
Correctness of physical principles
Evaluation of the caption & image
Artistic value
Degree of insight presented
How well your output image can capture and illustrate the project's main idea
Caption should clearly describe what is being plotted and what the viewer can learn from your image
Send your submissions to: sever741 at umn dot edu and tlow at umn dot edu.
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