Michael DeMarco: A Commuting Projector Model for Hall Conductance

Channel:
United States QuICS
Subscribers:
2,520
Published on ● Video Link: https://www.youtube.com/watch?v=E10AprHMbUQ


Duration: 57:39
210 views
0

Commuting projector models (CPMs) have provided microscopic theories for a host of gauge theories and are the venue for Kitaev’s toric code. An immediate question that arises is whether there exist CPMs for the Hall effect, the discovery of which ignited a revolution in modern condensed matter physics. In fact, a no-go theorem has recently appeared suggesting that no CPM can host a nonzero Hall conductance. In this talk, we present a CPM for just that: U(1) states with nonzero Hall conductance. In the context of quantum computation, this corresponds to a stabilizer code where the degrees of freedom are U(1) rotors and the code is protected not by long-range entanglement, but instead by a U(1) symmetry. We evade the no-go theorem because of the countably infinite number of states per site, and along the way we illuminate certain aspects of the group cohomology approach to topological phases for continuous groups.



Other Videos By QuICS


2022-03-03Alexander Dalzell: Random quantum circuits transform local noise into global white noise
2022-02-25Samson Wang: QuICS Special Seminar
2021-12-02Tobias Osborne: Simulating conformal field theories
2021-12-02Nolan Coble: IQC-QuICS Math-CS Seminar
2021-11-29Mina Doosti: Quantum Physical Unclonable Functions and Their Comprehensive Cryptanalysis
2021-10-06Victor Albert: Overview of quantum research at UMD
2021-09-30Nicolas Delfosse: Improved quantum error correction using soft information
2021-05-05Tamara Kohler and Emilio Onorati: Fitting quantum noise models to tomography data
2021-04-14Sisi Zhou: Error-corrected quantum metrology
2021-03-28Martin Fraas: Quantized quantum transport in interacting systems
2021-03-12Michael DeMarco: A Commuting Projector Model for Hall Conductance
2021-03-09Daniel Stilck França: Limitations of optimization algorithms on noisy quantum devices
2021-03-09Robert Huang: Fundamental aspects of solving quantum problems with machine learning
2020-11-04Wolfgang Pfaff: Increasing connectivity and modularity in superconducting quantum circuits
2020-10-29Iordanis Kerenidis: Quantum Machine Learning: prospects and challenges
2020-10-21Urmila Mahadev: Classical homomorphic encryption for quantum circuits
2020-10-08Thomas Baker: Density functionals, Kohn-Sham potentials & Green’s functions from a quantum computer
2020-09-23James D. Whitfield: Limitations of Hartree-Fock with Quantum Resources
2020-09-18Mark Wilde: Quantum Renyi relative entropies and their use
2020-08-17Dmitry Green: A superconducting circuit realization of combinatorial gauge symmetry
2020-07-23Matt Hastings: The Power of Adiabatic Quantum Computation with No Sign Problem


Tags:
quantum computing