Shelby Kimmel

Research

Algorithms

I primarily study query problems, in which one tries to learn a property of an unknown function, by "querying" values of the function. The goal is to determine the property of the function using as few queries as possible. I try to prove upper and lower bounds on the number of queries needed by a quantum algorithm to solve the problem. This is a rewarding model to work in because it is possible to prove that quantum computers require fewer queries than classical computers.

Algorithms Papers
S. Jeffery. S. Kimmel.
Quantum Algorithms for Graph Connectivity and Formula Evaluation.
Manuscript 2017
Arxiv
Bibtex
S. Kimmel, C. Y-Y. Lin, G. H. Low, M. Ozols, T. J. Yoder
Hamiltonian Simulation with Optimal Sample Complexity
Nature Partner Journals Quantum Information, vol 3, no. 13, 2017.
Journal
Arxiv
Bibtex
E. Farhi, S. Kimmel, K. Temme.
A Quantum Version of Schöning's Algorithm Applied to Quantum 2-SAT.
Quantum Information and Computation, vol 16, no. 13-14, 2016.
Journal
Arxiv
Bibtex
S. Kimmel, C. Y. Y. Lin, H. H. Lin.
Oracles with Costs.
Proceedings of Theory of Quantum Computing 2015. pp 1-26.
Proceedings
Arxiv
Bibtex
A. M. Childs, S. Kimmel, R. Kothari.
The Quantum Query Complexity of Read-Many Formulas.
Proceedings of ESA 2013, pp 337-348.
Proceedings
Arxiv
Bibtex
S. Kimmel
Quantum Adversary (Upper) Bound.
Chicago Journal of Theoretical Computer Science, vol 2013 n 4. And Proceedings of ICALP. 2012 pp 557-568.
Journal
Arxiv
Bibtex
B. Zhan, S. Kimmel, A. Hassidim.
Super-polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure.
Proceedings of ITCS, pp 249-265. 2012
Proceedings
Arxiv
Bibtex

Process Tomography

We don't yet have scalable quantum computers because errors in current systems grow more quickly than we can correct them. The ability to accurately characterize these errors is important for experimentalists as they try to improve their systems. I create tools that provide information about these errors in ways that are accurate, efficient, and make realistic assumptions about experimental resources.

Process Tomography Papers
K. Rudinger, S. Kimmel, D. Lobser, P. Maunz.
Experimental demonstration of cheap and accurate phase estimation.
Manuscript 2017
Arxiv
Bibtex
S. Kimmel, Y.-K. Liu.
Quantum Compressed Sensing Using 2-Designs.
Manuscript 2015. (Accepted to SAMPTA 2017.)
Arxiv
Bibtex
S. Kimmel, G. H. Low, T. J. Yoder.
Robust calibration of a universal single-qubit gate set via robust phase estimation.
Phys. Rev. A 92 (6), 062315. 2015.
Journal
Arxiv
Bibtex
B. R. Johnson, M. P. da Silva, C. A. Ryan, S. Kimmel, J. M. Chow, T. A. Ohki.
Demonstration of Robust Quantum Gate Tomography via Randomized Benchmarking.
New Journal of Physics 17 (11), 113019. 2015.
Journal
Arxiv
Bibtex
S. Kimmel, M. P. da Silva, C. Ryan, B. Johnson, T, Ohki.
Robust Extraction of Tomographic Information via Randomized Benchmarking.
Physical Review X, 2014, vol 4, n 1, pp 011050, 2014.
Journal
Arxiv
Bibtex

Computational Complexity, Information Theory, and Eclipses

In the area of complexity theory, I am most interested in understanding whether quantum proofs are more powerful than classical proofs. In other words, if someone tries to convince me that a statement is true by giving me a proof, in what cases is it helpful for that proof to be a quantum state rather than a classical bit string? In information theory, I have investigated how entanglement can be used as a resource to perform quantum measurements between separated parties. Finally, as an undergrad, I did some eclipse chasing, studying the solar corona.

Computational Complexity, Information, and Eclipse Papers
B. Fefferman, S. Kimmel
Quantum vs Classical Proofs and Subset Verification.
Manuscript 2015
Arxiv
Bibtex
S. Bandyopadhyay, G. Brassard, S. Kimmel, W. Wootters.
Entanglement Cost of Nonlocal Measurements.
Phys. Rev. A. vol 80, n 1, pp 012313. 2009.
Journal
Arxiv
Bibtex
J. Pasachoff, S. Kimmel, M. Druckmuller, V. Rusin, M. Saniga.
The April 8, 2005 Eclipse White-light Corona.
Solar Physics. vol 238, n 2, pp 261-270, 2006.
Journal
Bibtex