A unified framework of transformations based on the Jordan-Wigner transformation

Abstract: Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of transformations mapping fermionic systems to qubit systems is presented, and many existing transformations, such as Jordan-Wigner, Bravyi-Kitaev, and parity transformations, are included in this framework. Based on this framework, the Multilayer Segmented Parity (MSP) transformation is proposed. The MSP transformation is a general mapping with an adjustable parameter vector, which can be viewed as a generalization of the above-mentioned mappings. Furthermore, the MSP transformation can adjust flexibly when dealing with different systems. Applying these mappings to the electronic structure Hamiltonians of various molecules, the MSP transformation is found to perform better on the number of Pauli operators and gates needed in the circuit of Hamiltonian simulation. The MSP transformation will reduce the qubit gate requirement for Hamiltonian simulation on noisy intermediate-scale quantum devices,and it will provide a much wider choice of mappings for researchers.