Quantum Error Correction and Mathematical Physics

Elizabeth Crosson, University of New Mexico Quantum Information and Computing
January 7, 2019 3:00 pm LSK 460

Error correcting codes protect information by encoding it into a larger system with some redundancy, allowing the original logical information to be recovered even if part of the encoded system becomes lost or corrupted. In this talk, I will introduce the theory of quantum error correcting codes (QECC), which depart from the classical case in surprising and beautiful ways in order to surmount some uniquely quantum hurdles: quantum information cannot be copied, and general measurements will disturb quantum states. The success story of QECC culminates in the proof that they enable fault-tolerant quantum computation, overcoming the inherent fragility of quantum states and operations. But apart from this central application in quantum computation, there is also a link between QECC and condensed matter physics, which comes from the correspondence between locally checkable codes and local interactions in quantum spin models. This correspondence is relatively well-studied in the case of topologically ordered systems with a finite spectral gap, but in this talk I will also describe recent work on the frontier of this subject which finds QECC in the low energy space of gapless quantum spin chains, as well as QECC with nearly optimal parameters in the ground space of high dimensional gapless local Hamiltonians.

Bio: Elizabeth Crosson is an Assistant Professor of Physics at the University of New Mexico’s Center for Quantum Information and Control. Prior to joining UNM in 2018, Crosson earned her PhD in physics at the University of Washington in 2015, and then spent three years as a postdoc at the Caltech Institute for Quantum Information and Matter. Her research involves several topics from the theory of quantum computation, including quantum algorithms, Hamiltonian complexity theory, rigorous classical simulations of quantum spin systems, and quantum error correction.