I will present our latest results concerning the fermion-to-spin mapping investigated in my research group. Simulating a fermionic system on a quantum computer requires encoding the anti-commuting fermionic variables into the operators acting on the qubit Hilbert space. The most familiar of which, the Jordan-Wigner transformation, encodes fermionic operators into non-local qubit operators. As non-local operators lead to a slower quantum simulation, our recent works have proposed ways of encoding fermionic systems into strictly local qubit operators. The latest work describes a family of strictly local encoding. This is a general construction for designing quantum codes for fermionic simulation that is capable of adapting to suit the problem and resources at hand. We expect that the encoding construction presented will find use in quantum simulation experiments ranging from quantum chemistry, to quantum gravity, to condensed matter physics
