Application of Generalized Symmetry in Quantum Computation

Abstract: I will discuss applications of generalized symmetry in fault-tolerant quantum computation. Symmetry can serve as logical gates in quantum codes, and generalized symmetries provide wide variety of logical gates implemented by constant depth circuits. These logical gates are unitary operators given by symmetry-protected topological responses labelled by group cohomology and can be expressed explicitly on the lattice using cohomology operations including cup product, Steenrod squares and new combinations of higher cup products called higher Pontryagin powers. Implementing these gates could make it more efficient to compile specific types of quantum algorithms such as Shor’s algorithm. We further extend the construction to quantum codes with boundaries, which generalizes the folding approach in color codes, and generalize the discussion to good LDPC codes.

condensed mattergeneral relativity and quantum cosmologyHEP - latticeHEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

Quantum Theories of Fields, Matter, and Strings

Series comments: A series of talks covering a broad range of topics in theoretical physics, including high energy theory, condensed matter, and string theory.

To receive the Zoom link, please fill out the following form:

Mail List: docs.google.com/forms/d/1KmOdB7a8Z3vH9mRJsPT9pr0Ej0Qj7dMI9I1JKEEiYzI/edit

Recordings are available on our YouTube channel: www.youtube.com/@QTFMS