The interplay of topology, quantum information, and condensed matter physics has emerged as one of the most fascinating and quickly developing areas of modern research. In Philip Anderson’s famous 1972 article “More is Different,” he describes how the collective behavior of large complex aggregates can drastically differ from that of the constituents. Typically these macroscopic behaviors are distinguished by local symmetry breaking order parameters. A famous counterexample came with the discovery of the quantum Hall effect, where distinct phases enjoyed the same symmetries and thus could not be fully charecterized by local order parameters alone. This discovery marked the introduction of topological phases of matter and triggered decades of research on the subject. Topological phases provide an organizing framework for a wide variety of problems from the quantum Hall effect to error-correcting codes.
Inherently robust to local perturbations, topological phases furnish platforms well-suited for fault-tolerant quantum computation. Quantum computers are one of the major driving forces of research on topological phases today and promise a wide range of applications from testing modern security protocols to quantum simulators that can predict the physics of real systems beyond the capabilities of any classical computer. Realizing this potential is burdened by many fundamental challenges such as environmental noise. One resolution exploited in nearly all quantum computing platforms is the use of topology—at its core, one delocalizes quantum information over space, ensuring that it is insensitive to local perturbations.
Inspired by the need for realistic blueprints of quantum computing hardware, my research spans several areas of topological quantum condensed matter physics. On the practical side, I propose realizations of topological phases and highlight their applications toward quantum computing technologies. And on the more formal end, I characterize and classify topological phases by developing the fundamental mathematics underpinning their description. The wordcloud below gives a general sense of my interests.
David Aasen, Parsa Bonderson, Christina Knapp.Torsorial actions on G-crossed braided tensor categories. arXiv:2107.10270
Kai Klocke, David Aasen, Roger S. K. Mong, Eugene A. Demler, Jason Alicea. Time-domain anyon interferometry in Kitaev honeycomb spin liquids and beyond. arXiv:2011.00015
David Aasen, Paul Fendley, Roger S. K. Mong. Topological Defects on the Lattice: Dualities and Degeneracies. arXiv:2008.08598
David Aasen, Daniel Bulmash, Abhinav Prem, Kevin Slagle, Dominic J. Williamson. Topological Defect Networks for Fractons of all Types. arXiv:2002.05166
David Aasen, Roger S. K. Mong, Benjamin Hunt, David Mandrus, Jason Alicea. Electrical probes of the non- Abelian spin liquid in Kitaev materials. arXiv:2002.01944
Kevin Slagle, David Aasen, Dominic Williamson. Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order. arXiv:1812.01613
David Aasen, Ethan Lake, Kevin Walker. Fermion condensation and super pivotal categories. arXiv:1709.01941
David Aasen, Shu-Ping Lee, Torsten Karzig, Jason Alicea. Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade. arXiv:1606.09255
Ryan V. Mishmash, David Aasen, Andrew P. Higginbotham, Jason Alicea. Approaching a topological phase transition in Majorana nanowires. arXiv:1601.07908
David Aasen, Roger S. K. Mong, Paul Fendley. Topological Defects on the Lattice I: The Ising model. arXiv:1601.07185
David Aasen, Michael Hell, Ryan V. Mishmash, Andrew Higginbotham, Jeroen Danon, Martin Leijnse, Thomas S. Jespersen, Joshua A. Folk, Charles M. Marcus, Karsten Flensberg, Jason Alicea. Milestones toward Majorana-based quantum computing. arXiv:1511.05153
David Aasen, Tejal Bhamre, Achim Kempf. Shape from sound: toward new tools for quantum gravity. arXiv:1212.5297
Eduardo Martin-Martinez, David Aasen, Achim Kempf. Processing quantum information with relativistic motion of atoms. arXiv:1209.4948
David Aasen, Stefano Chesi, W. A. Coish. Quasiparticle velocities in 2D electron/hole liquids with spin-orbit coupling. arXiv:1110.6661