This award supports theoretical research and education to study two fields where computer simulations can give important information: quantum computers and spin glasses.
It is well known that there are certain specialized problems which can be solved much more efficiently on a quantum computer than on a classical computer. The question addressed in this project is whether an eventual quantum computer could, in addition, solve a broad range of optimization problems more efficiently than a classical computer using the Quantum Adiabatic Algorithm. Results already obtained by the PI for several optimization problems indicate that the simplest application of this algorithm does not give an improvement over classical algorithms for large problem sizes. The PI will therefore use the inherent flexibility of the quantum adiabatic algorithm to see if modifications to it give a significant improvement, and also apply the algorithm to other types of problem. In particular, the PI will investigate if quantum algorithms will be helpful in the field of machine learning.
The PI will also investigate several questions in the field of spin glasses, which are systems with disorder and frustration. The study of spin glasses is important far beyond the rather narrow field of dilute magnetic alloys where they were first studied, because ideas developed for them have applicability to a wide range of complex systems, such as combinatorial optimization problems in computer science, protein folding in biology, and structural glasses (e.g. window glass). Spin glasses are a convenient system in which to study this class of problems since they can be probed in fine detail in experiments by applying a magnetic field, and can be represented theoretically by simplified models which are amenable to computer simulation. Understanding spin glasses will help our understanding of these other problems as well. In particular, the PI will apply optimization methods developed using spin glass ideas to solve other optimization problems.
This award will support the education of students in developing state-of-the-art algorithms for large-scale numerical simulations. The research will enable them to pursue scientific careers in many related fields and become part of a scientifically sophisticated workforce. Recent students of the PI have gone on to apply the ideas learned under his supervision in both academia and industry. The PI will also continue to teach techniques used in his research as part of courses on computational physics, which are offered to both undergraduates and graduate students.
NON-TECHNICAL SUMMARY
This award supports theoretical research and education to study two fields where computer simulations can give important information: quantum computers and spin glasses
Information in a computer is stored as "bits" which take values 1 or 0. It has been proposed that certain problems could be solved more efficiently on a quantum computer in which the bits are replaced by "qubits" which follow the laws of quantum mechanics and can be simultaneously in states 1 and 0, which is called a superposition. So far, it has proved very difficult to build a useful quantum computer because a small amount of external noise destroys superposition. However, it is still of interest to study what problems could be solved efficiently on a quantum computer if and when a quantum computer can be built. The PI will study whether a particular broad class of problems, known as optimization problems, can be solved more efficiently on a quantum computer than on a classical computer. Since we do not have a quantum computer, the PI will emulate the behavior of a quantum computer by doing numerical simulations on a classical computer.
The PI will also study a class of systems called "spin glasses" which exhibit glassy behavior at low temperatures, that is, they do not come to equilibrium but are always evolving with time. Ideas developed for spin glasses have applicability to a wide range of complex systems, such as some optimization problems in computer science, protein folding in biology, and structural glasses (e.g. window glass). Spin glasses are a convenient system in which to study this class of problems since they can be probed in fine detail in experiments, and can be represented theoretically by simplified models which are amenable to computer simulations. Understanding spin glasses will help our understanding of these other problems as well.
This award will support the education of students in developing state-of-the-art algorithms for large-scale numerical simulations. The research will enable them to pursue scientific careers in many related fields and become part of a scientifically sophisticated workforce. Recent students of the PI have gone on to apply the ideas learned under his supervision in both academia and industry. The PI will also continue to teach techniques used in his research as part of courses on computational physics, which are offered to both undergraduates and graduate students.
