Majorana tensor decomposition: a unifying framework for decompositions of fermionic Hamiltonians to linear combination of unitaries

Linear combination of unitaries (LCU) decompositions have become a key tool for encoding operators on quantum computers, enabling efficient implementations of arbitrary operators. In particular, LCU methods provide a way to encode the electronic structure Hamiltonian into quantum circuits. Over the years, various decomposition techniques have been developed for this purpose. Here, we introduce the Majorana tensor decomposition, a framework that unifies existing LCU approaches and introduces novel decompositions using low-rank tensor factorizations. We benchmark a range of decomposition techniques on small molecular systems and hydrogen chains of increasing sizes, evaluating their performance across different LCU methods.