Project Info
Solving quantum many-body systems using neural networks
Zhexuan Gong | gong@mines.edu
Quantum many-body systems are ubiquitous in modern physics, ranging from atomic, molecular, and optical physics to condensed matter physics and quantum information. Even in the simplest case where a quantum many-body system is made of a number of two-level quantum systems (spin-1/2s or qubits), solving such system is notoriously difficult because the Hilbert space dimension scales exponentially with the number of particles. With traditional methods, the most powerful classical computers nowadays cannot solve the Schrodinger’s equation for a quantum many-body system made of just 50 spin-1/2s. This makes the prediction of quantum materials’ properties difficult, because there are far more than 50 spin-1/2s in a real material.
In the last year, a novel approach of solving large quantum many-body systems is invented and brought under the spotlight. This approach uses neural networks and machine learning to solve the Schrodinger’s equation. For certain specific systems, such approach has shown to be signficiantly faster than other existing approaches, making it possible to predict the behaviors of hundreds or even thousands of spins.
However, this new approach is still in an early stage. Existing algorithms adopting this approach are neither very efficient nor very robust. Moreover, there is a severe lack of understanding on what types of quantum many-body systems suit this new method and what types do not. Thus many open questions remain to be addressed.
In this project, the student will aim to improve existing algorithms to make them faster or more robust, and write high-quality codes to implement the algorithms. The potential outcome of the research can bring valuable contributions to many researchers in this community.
More Information
http://science.sciencemag.org/content/355/6325/602
http://www.nature.com/doifinder/10.1038/nphys4035
http://www.nature.com/doifinder/10.1038/nphys4037
Student Preparation
Qualifications
The student should have taken Modern Physics I. Students that have taken Modern Physics II or have learned the framework of quantum mechanics themselves will be highly preferred. Students with good programming skills and basic knowledge of machine learning are also preferred.
Time Commitment
20 hours/month
Skills/Techniques Gained
The student will learn basics of condensed matter physics to study quantum many-body systems and basics of machine learning and neural network to understand the computational approach. The student can greatly improve their programming skills and mathematical modeling skills during the course of this research. More importantly, the student will learn how to think creatively in a research project, how to seek help from a variety of resources, and how to communicate in a research-focused environment.
Mentoring Plan
I plan to meet with the student once every week or every two weeks, depending on the student’s progress. I will also offer help to the student whenever a road block is met. The course of the project will be divided into three stages:
In the first stage of the research, the student will learn necessary background materials on machine learning and condensed matter physics (in particular spin models). In the second stage of the project, the student will focus on systems that have exact solutions. This allows one to easily check whether an algorithm is correctly working. Moreover, with a good understanding of the physical system, it is more likely to find ways to improve existing algorithms’ performance. For example, the learning rate of an algorithm can be adaptively changed during the evolution of the Schrodinger’s equation, and stochastic algorithms can be used to greatly speedup the calculations. In the last stage of the project, the student will apply the developed algorithm or code library to real quantum many-body systems that have no known solutions, e.g. frustrated spin models in a two-dimensional lattice that have puzzled condensed matter physicists for decades.