The talk discusses the relationship between fermionic observables and Pauli matrices on two-dimensional lattices. First, it will introduce the exact bosonization method. It is argued that all fermion-to-qubit mappings can be obtained from this exact bosonization via a Clifford finite-depth generalized local unitary circuit. The argument is based on the properties of quantum cellular automata in two dimensions. Next, we use this principle to construct novel fermion-to-qubit mappings with smaller qubit-fermion ratios. As the ratio approaches 1, the mapping becomes the 1d Jordan-Wigner transformation embedded in the 2d lattice. It will also demonstrate that several known methods and models, like the Bravyi-Kitaev superfast simulation and the Majorana loop stabilizer codes, can be derived from the exact bosonization.
Yu-An Chen is an assistant professor at the Center for Quantum Materials Science, School of Physics, Peking University. He obtained Bachelor in Mathematics and Physics from the Massachusetts Institute of Technology (MIT) in June 2015. He received his Ph.D. in Physics from the California Institute of Technology (Caltech) in June 2020. He once served as a Research Scientist in Google's Quantum AI research team. From September 2020 to June 2023, he was a postdoctoral researcher at the Joint Quantum Institute of the University of Maryland, College Park.
He conducted in-depth research on bosonization (mapping fermions to boson systems), extending the exact one-dimensional bosonization (Jordan-Wigner transformation) to any higher dimension, and introducing essential concepts of algebraic topology and field theory. Using insights from high-energy physics combined with the structure of algebraic topology, he derived the significant "fermion-boson" duality in condensed matter, facilitating quantum simulation and construction of topological phases and decomposing the time evolution of the Hamiltonian into quantum circuits. He was invited to join Google to design quantum simulations for various fermion models. His research involves topological phases, gravitational anomalies, Pauli stabilizer error correction codes, quantum cellular automata, and fermion error correction codes.