2022/12/30(Fri) 10:30 -12:00 五樓第一會議室 5F, 1st Meeting Room
Title
Exact bosonization in all dimensions
Speaker
陳昱安博士 (Joint Quantum Institute, University of Maryland) Dr. Yu-An Chen (Joint Quantum Institute, University of Maryland)Abstract
This talk introduces the exact bosonization (generalized Jordan–Wigner transformation) in arbitrary dimensions. The exact bosonization maps fermionic systems to spin models (a new class of Z2 gauge theories) via the stabilizer code formalism. This mapping preserves the locality and explicitly depends on the choice of spin structure. This exact bosonization utilizes Kitaev's surface code (toric code) and imposes the gauge constraint to restrict onto the subspace of emergent fermions. We identify the algebra of physical fermions with the sub-algebra of Pauli matrices generated by the emergent fermions in Kitaev's surface code. This construction corresponds to the topological Chern-Simon action for (2+1)D and the Steenrod square action for general dimensions in the spacetime picture. Our bosonization directly connects topological quantum field theories and quantum codes. For fermionic quantum simulation, we can optimize various properties of fermion-to-qubit mappings, i.e., the code distance and the qubit-fermion ratio.
References:
Annals of Physics 393, 234-253 (2018) (https://arxiv.org/abs/1711.00515)
Physical Review B 100 (24), 245127 (2019) (https://arxiv.org/abs/1807.07081)
Physical Review Research 2 (3), 033527 (2020) (https://doi.org/10.1103/PhysRevResearch.2.033527)
arXiv:2201.05153 (https://arxiv.org/abs/2201.05153)
arXiv:2210.08411 (https://arxiv.org/abs/2210.08411)
Language
演講語言 (Language): in English