Pauli Decomposition over Commuting Subsets: Applications in Gate Synthesis, State Preparation, and Quantum Simulations

A key task in quantum computation is the application of a sequence of gates implementing a specific unitary operation. However, the decomposition of an arbitrary unitary operation into simpler quantum gates is a nontrivial problem. Here we propose a general and robust protocol to decompose any target unitary into a sequence of Pauli rotations. The procedure involves identifying a commuting subset of Pauli operators having a high trace overlap with the target unitary, followed by a numerical optimization of their corresponding rotation angles. The protocol is demonstrated by decomposing several standard quantum operations. The applications of the protocol for quantum state preparation and quantum simulations are also described. Finally, we describe an NMR experiment implementing a three-body quantum simulation, wherein the above decomposition technique is used for the efficient realization of propagators.