## Graduate Research

[Work in progress]

This is fascinating for countless reasons. First, like when Albert Einstein realized Newton's laws were only approximate descriptions of reality that are correct in limiting cases (v << c), we've realized there's more to information than we initially thought. Classical information (bits) is merely a limiting case of quantum information (quantum bits) in the same way classical mechanics is a limiting case of special relativity. (The limiting case is when a quantum bit interacts with its environment and becomes classical.)

If this isn't already cool enough, there are algorithms for quantum computers that can solve problems faster than the best classical computers. Recently, advancements in experimental physics and engineering have led to the first generation quantum computers. These are nascent devices that aren't any more powerful than a mediocre cell phone, but the idea of building bigger, better quantum computers is very exciting. It's still a very hard engineering problem, but there have been significant "hardware" advancements in recent years. My research is about improving and adapting the "software" (algorithms) of quantum computers so that we can effectively use these first and second generation quantum computers.

**Semi-technical description:**My general dissertation area is (gate model) quantum algorithms, with a particular emphasis on near-term algorithms and applications for quantum computers. I'm interested in simulation algorithms for the many body problem, including chemical systems and quantum field theories. I think this is the most promising application for NISQ computers, but am also interested in areas beyond this, such as quantum machine learning and quantum signal processing. Quantum deep learning may be promising, but we might need another buzz word for this to happen. I like to try and solve the many problems variational quantum algorithms have created, such as optimization, scalability, and how to know I'm picking the right ansatz (we get along but I'm not sure it has everything I want, maybe I'd be better with a different ansatz, if it contained my state I think I'd know by now). I'm also very interested in query model quantum algorithms, and may have thought about the non abelian hidden subgroup problem for some time. From the perspective of programming languages, I find it fascinating to think about quantum programming and quantum software, and often argue that programming should have a bigger emphasis in our field--say, a bigger emphasis than summoning magical QRAM to get speedups. I realize I may have too many interests.

**Less technical description:**I do research in quantum computing, a model of computation that processes quantum bits of information rather than classical bits of information. What does that mean? Every computer, whether it be electrical like a standard laptop or a mechanical machine using marbles, works by processing information. For the large majority of history, this information was stored in physical systems that are described by the laws of classical mechanics. In this case, the information is stored in binary digits, or bits. In the 1980s, after the advent of quantum mechanics in the 1920s, people like Richard Feynman begin to think about storing information in physical systems that can only be accurately described by the laws of quantum mechanics. In this case, information is stored in quantum bits, or qubits. A quantum computer is still a device that processes information, but the information is quantum.This is fascinating for countless reasons. First, like when Albert Einstein realized Newton's laws were only approximate descriptions of reality that are correct in limiting cases (v << c), we've realized there's more to information than we initially thought. Classical information (bits) is merely a limiting case of quantum information (quantum bits) in the same way classical mechanics is a limiting case of special relativity. (The limiting case is when a quantum bit interacts with its environment and becomes classical.)

If this isn't already cool enough, there are algorithms for quantum computers that can solve problems faster than the best classical computers. Recently, advancements in experimental physics and engineering have led to the first generation quantum computers. These are nascent devices that aren't any more powerful than a mediocre cell phone, but the idea of building bigger, better quantum computers is very exciting. It's still a very hard engineering problem, but there have been significant "hardware" advancements in recent years. My research is about improving and adapting the "software" (algorithms) of quantum computers so that we can effectively use these first and second generation quantum computers.

## Undergraduate Research

At the University of Michigan, Ann Arbor, I worked with Dr. Yaoyun Shi on quantum computing during and after my senior year. I surveyed the field and studied in particular analog and digital quantum simulation. This was my first research experience in quantum computing.

Before my quantum days, I spent two summers at Michigan Technological Research Institute where I worked on software development, Fourier analysis, machine learning, and other problems.

Also during my undergraduate degree, I did many individual research projects for courses, a sample of which are included below.

Before my quantum days, I spent two summers at Michigan Technological Research Institute where I worked on software development, Fourier analysis, machine learning, and other problems.

Also during my undergraduate degree, I did many individual research projects for courses, a sample of which are included below.

Proof of photons, quantum entanglement, and local realism.Abstract: Two experiments in quantum mechanics are performed: spontaneous parametric downconversion and proof of single photon existence. In the former, we achieve coupled photon states and verify a Gaussian distribution of photon count rate vs. detector angle. In the latter, with a three detector assembly we measure the degree of second order coherence $g^{(2)}(0) = 0.0404 \pm 0.1368$ and thereby experimentally demonstrate the existence of photons. By performing a two detector measurement, we reaffirm the classical prediction of $g^{(2)}(0) \ge 1$ and regain the wave nature of light. In addition, other possible experiments that could be performed with a similar experimental setup, such as quantum entanglement and local realism, are discussed.This project was one of three individual experiments performed for Physics 442, Advanced Laboratory II (paper). I also gave a final presentation on one aspect of this experiment (slides). |

Cosmological expansion and dark energy.Abstract: Nearly all light observed from distant stellar objects is redshifted -- not from relative motion but from expansion of the cosmos itself. In the 1920s, Edwin Hubble observed that redshift is proportional to distance, and in 2011 the Nobel prize in physics was awarded for the discovery of the accelerating expansion of the universe through observations of distant supernovae. A proposed cause of this accelerated expansion is dark energy, a mysterious form of matter that doesn't interact with light and pushes things apart. Dark energy could have serious implications about the genetic makeup of the cosmos, its origins, and its fate.This presentation was given as a final research project for Physics 391, Modern Physics Laboratory. (slides) |

Ion containment with magnetic bottles.Abstract: Ion containment is important to several branches of science, including physics and chemistry. Using vPython, this paper explores the motion of charged particles in a magnetic bottle, a type of magnetic mirror created by two current-carrying coils. The magnetic field is calculated and displayed inside of the bottle, and trajectories of ions that do and do not get trapped are shown. The velocity criteria of trapped particles is explored as well as other initial conditions (such as charge and initial position) that determine whether or not an ion gets trapped.This research constituted the final project for Physics 260, Electricity and Magnetism. (paper) |