Alexander Meill, Ph.D.
Ph.D. Physics, University of California, San Diego (2019)
M.S. Physics, University of California, San Diego (2015)
B.A. Physics, Dartmouth College (2013)
Dr. Meill joined the department of sciences in Fall 2019. In the near term he will be teaching courses from the engineering physics track at Wentworth, but he is also working to develop an elective course on quantum information and quantum computing. Dr. Meill’s research focuses on the fundamental properties of quantum mechanics, with particular attention to the phenomenon of quantum entanglement. He uses mathematical and physical symmetries to develop our understanding of challenging problems in quantum information science.
Dr. Meill is additionally interested in various aspects of education research, including methods for student feedback, classroom observation pedagogy, and open-ended physics lab development and implementation.
With the development of quantum mechanics came the discovery of many surprising and powerful consequences of the new theory. Quantum entanglement has become one of the most prevalent, exciting, and heavily researched of those aspects. It describes a linking between particles which ties their behaviors to each other despite potentially being on opposite sides of the universe. That link can be used to transmit information securely, perform computational tasks faster than standard computers, and could potentially even tell us about the fundamentals of what governs our universe. Understanding the limits and properties of entanglement, though, is mathematically challenging.
My research makes that challenge more approachable by restricting the calculations to quantum systems which obey convenient symmetries. For instance, if the particles are arranged on a ring, the entanglement between them will only depend on their spacings on the ring. Shown below are the achievable regions of those entanglements for rings of 4 and 5 particles.
I have examined these kinds of problems in fully symmetric particle webs, translationally invariant rings, tensor networks, and quantum random walks. The work involves computational simulation of large quantum systems and extensive mathematical work, including various analytical techniques in geometry and linear algebra, as well as group theoretic and combinatoric depictions of symmetries.
Quantum information science is one of the fastest growing areas of physics, and I have plenty of projects for students to work on, so please reach out to me if you are interested!
A. Meill and D. M. Meyer, “Mean Field Approximation for Identical Bosons on the Complete Graph”. arXiv:1910.14521
A. Meill and D. M. Meyer, “Pairwise Concurrence in Cyclically Symmetric Quantum States”. arXiv:1802.06877
A. Meill and D. M. Meyer, “Symmetric 3 Qubit State Invariants”. arXiv:1702.07295
2018-19 Barbara and Paul Saltman Excellent Teaching Award for Graduate Students
Entanglement Properties of Quantum Random Walks (2019). Southwest Quantum Information and Technology Workshop. Albuquerque, New Mexico.
Entanglement Constraints in Various Symmetric Quantum Systems (2018). Southwest Quantum Information and Technology Workshop. Santa Fe, New Mexico.