Majorana Tensor Decomposition: A unifying framework for decompositions of fermionic Hamiltonians to Linear Combination of Unitaries

Abstract: Linear combination of unitaries (LCU) decompositions have appeared as one of the main tools for encoding operators on quantum computers, allowing efficient implementations of arbitrary operators. In particular, LCU approaches present a way of encoding information from the electronic structure Hamiltonian into a quantum circuit. Over the past years, many different decomposition techniques have appeared for the electronic structure Hamiltonian. Here we present the Majorana Tensor Decomposition (MTD), a framework that unifies existing LCUs and offers novel decomposition methods by using popular low-rank tensor factorizations.