Efficient Hamiltonian Encodings for Simulation of Interacting Fermions

In many scenarios for simulating interacting fermionic systems on quantum computers, such as finding the eigenstates or simulating the time evolutions, the first step is to encode the physical Hamiltonian into qubit operators. Existing encoding procedures such as the Jordan-Wigner transformation and Bravyi-Kitaev transformation are not resource efficient because they encode each second-quantized fermionic operator into a Pauli string, without incorporating the structure of the Hamiltonian in question. We present a novel general framework to directly relate different fermion-to-qubit encoding schemes, and apply it to ab initio electronic structure Hamiltonians, which reduce the total number of gates for quantum chemistry simulations.