In order to simulate interacting fermionic systems on quantum computers, 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 general framework that encompasses all encoding schemes that map n fermions to n qubits, and develop an optimization algorithm with Clifford transformations on top of this framework. This successfully recovers known optimal results for solvable models, and consistently reduces the Pauli weight by 15–20% for other models.

Pizza and drinks will be served after the seminar in ATL 2117.