1:30 pm MCP 201
Exact bosonization in higher dimensions: from higher group bosonic SPT (symmetry protected topological) phases to Gu-Wen fermionic SPT phases.
Yu-An Chen, Caltech
The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any simply connected manifold in 2d and 3d. This gives a duality between any fermionic systems and a new class of 
lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is exactly equivalent to adding topological terms (Chern-Simon term in 2d or the Steenrod square term in 3d) to the Euclidean action. We can increase the code distance of this mapping, such that this mapping can correct all 1-qubit and 2-qubits errors and is useful for the simulation of fermions on the quantum computer. The second part of my talk is the application of this boson-fermion duality on SPT phases. By the boson-fermion duality, we are able to show the equivalent between any supercohomology fermionic SPT and some higher-group bosonic SPT phase. Particularly in (3+1)D, we have constructed a unitary quantum circuit for any supercohomology fermionic SPT state with gapped boundary construction. This fermionic SPT state is derived by gauging higher-form symmetry in the higher-group bosonic SPT and ungauging the 
fermion parity. The bulk-boundary correspondence in (3+1)D fermion SPT phases will also be briefly discussed.