Scientific Research
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Quantum Communication
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Mentor
Alexander Korotkov Products 1 dissertation chapter 1 conference presentation |
I did some work on modeling a quantum information transfer protocol proposed by my PhD adviser. I quantitatively studied the effects of decoherence on the efficiency of transfer assuming that the procedure is implemented using the so-called RezQu quantum computing architecture proposed by the Martinis group at University of California, Santa Barbara.
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Quantum Error Correction
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Mentor
Alexander Korotkov Products 1 dissertation chapter 1 peer-reviewed journal article 1 conference presentation |
I am preparing a manuscript for publication about currently realizable quantum error correction procedures for superconducting phase qubits. Although experiments in other superconducting systems have recently appeared, their main purpose is a proof-of-principle demonstration of quantum error correction; whereas my paper will look at procedures that can be implemented in a laboratory for real-world improvement of the storage capacity for quantum information. There are slides from a conference talk I gave on this subject available in the Presentations section of this website.
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Weak Quantum Measurements
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Mentor
Alexander Korotkov Products 1 dissertation chapter 1 peer-reviewed journal article 1 conference presentation |
In quantum mechanics courses through the usual curriculum students are rarely taught about partial measurement. I do not believe this is a major tragedy since most of the time full measurement is performed. However, the lack of exposure to the subject of weak measurement seems to have left a gap in scientists understanding of the fundamentals of quantum mechanics. Also, since experiments rely on ensemble averages of multiple repeated projective measurements on similar operational procedures for tomographic verification, many people believe that the inherent randomness of quantum systems is the fundamental understanding. Converse to this assertion, quantum computing has shown us that the inner workings of the state description (wavefunction or density matrix) can have real effects on the final outcome of a single projective measurement after certain sequences of operations (quantum algorithms). The importance of these subtle differences in the philosophical interpretations of measurement's role in quantum mechanics may not at first seem important, but it is my belief that they allow us a deeper ability to engage in what I call quantum engineering (the use of the principles of quantum mechanics to achieve certain operational/computational goals, such as efficiently searching in an unsorted database or securely transmitting a cryptographic key). My work so far in Weak measurement has revolved around weak measurement reversal (also known as "uncollapsing").
As an introductory project when I began working with Dr. Korotkov I was asked to simulate a simple uncollapsing experiment that was performed by John Martinis' group at the University of California, Santa Barbara. While simulating the experiment I started to generalize the parameters and found a unexpected result: I could increase the fidelity of the procedure by increasing one of the non-operational durations relative to the others. This phenomena was soon easily understood as the reversal of the state-description dynamics caused by energy relaxation of the system. We realized that this was an effective method to suppress the decoherence caused by energy relaxation and could be implemented using two partial measurements of a single qubit. This was a very interesting result since the only other decoherence suppression technique that used only one qubit is Dynamical Decoupling, which cannot protect against Markovian processes (energy relaxation is a Markovian process).
Early in 2011, an experimental group at POSTECH demonstrated our proposed procedure in a beautiful optical adaptation (our original was mentioned in the context of superconducting qubits). Their results were outstandingly close to our theoretical predictions and there paper was published in the journal Optics Express. After this accomplishment they extended the procedure to two entangled photons and showed that the procedure applied independently to each would in fact restore the entanglement lost to energy relaxation (this was expected and was mentioned as a footnote in our original paper). This is another very interesting effect, since even beyond the point of so-called entanglement sudden death (a premature disappearance of entanglement, even before full decoherence of the constituent subsystems), full entanglement can be restored to the photons.
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Frustrated Magnetism
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Mentor
Kirill Shtengel Products 1 lecture |
I first entered this topic with a very clear research question given to me by my advisor at the time, Dr. Kirill Shtengel: What is the ground state of 18 electrons on a Kagome lattice? Having sole responsibility over such a well-defined problem was a great joy for me. Dr. Shtengel was a wonderful mentor and gave a lot of his time introducing me to the conceptual techniques that we would later use in our search for a solution. Once I had an understanding of these techniques, it was off to the races. Well, it was off to the computer screen to start coding an algorithm to efficiently find the first stage of the solution. The task I performed was to find an array of all possible pairwise connections of 18 identical points equally spaced along the circumference of a circle. This was a really fun challenge and after considerable work I had a program that could do this task in a reasonable amount of time (it took about seven days continuous run time on my old laptop). The next stage was to turn this overcomplete basis into a orthonormal basis using a generalized Gramm-Schmidt procedure. This was a fairly straightforward program to build and I successfully completed this stage in the research. Although I found the topic stimulating and rewarding, I started to slip into a bit of a personal existential dilemma: I wanted to participate in the process of pure scientific inquiry, but I craved the stability of working toward a well-defined application. Over the years since this experience, I have come to believe that my primary purpose as a scientist is to maintain the chain of science, ethically employ my expertise in the use of funds given to me for this purpose, and to facilitate the progress of scientific discovery and understanding. However, as a young, idealistic developing scientist this desire for a stable purpose, and the discovery of Dr. Alexander Korotkov (a theoretical physicist working in the Electrical Engineering department), led me to my PhD work in Weak Measurements, Quantum Error Correction, Decoherence Suppression, and Quantum Communication.
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Self Assembly in Biophysics
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Mentor
Roya Zandi Products 1 lecture |
The first research topic in gradute school that I approached was Biophysics. I had a long-held desire to understand the human experience from a physics-guided computational viewpoint and hoped this would be a path to finding that understanding. My work in Biophysics was under the supervision and guidance of Dr. Roya Zandi, although my primary collaborator was a postdoctoral researcher named Artem Levandovsky. Artem had developed a code that calculated stable virus formations built from elementary components and I worked with him for about three months coding a subroutine that would characterize and statistically analyze the population proportions of different stable configurations. Our hope was to show that the population distributions found by his code were consistent with the population variations found in nature. Together we made some headway, but I decided to leave the group to pursue another opportunity that had opened up for me to work on a project that I felt would allow me to develop a ground up comprehension of my research. This was my first experience in theoretical research and I did not yet understand the process of making small incremental progress while mastery is concurrently acquired. I have since become more comfortable producing results while acquiring mastery. However, at the time I wanted to start with a project from the beginning; this desire led me to Frustrated Magnetism.
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Physics Education Research
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Mentor
Michael Loverude Products 1 slide for presentation |
I also worked with Dr. Michael Loverude on physics education research. I was in charge of interpreting and recording student responses on pedagogical-assessment quizzes. I would enter useful and relevant coded responses into a spreadsheet program for later statistical analysis.
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Electron Scattering
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Mentor
Murtadha Khakoo Products: 2 conference presentations 3 peer-reviewed journal articles |
While working toward my BS in physics, I was also a member of Dr. Murtadha Khakoo's electron scattering laboratory. I was involved in typical tasks such as data acquisition and analysis, equipment control and calibration, and on-the-fly troubleshooting and problem resolution. I also held a very special position as the only physics student with full access to the campus machine shop. After training with the campus's only employed machinist, David Parsons, I fabricated an entire vacuum-friendly rotary table for the angular study of differential electron cross sections scattered off of various polyatomic targets. This is the time in my life when I truly found a passion for physics as a philosophy of discovery and understanding of the natural world. To view my publications that resulted from my time in this lab, please see my Publications list or my Curriculum Vitae.
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