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

TL;DR

This paper introduces a robust method for decomposing any quantum unitary into Pauli rotations by identifying commuting subsets, enabling efficient quantum gate synthesis, state preparation, and simulations, demonstrated through experiments.

Contribution

It presents a general protocol for unitary decomposition into Pauli rotations using commuting subsets and numerical optimization, applicable to various quantum tasks.

Findings

Successfully decomposed standard quantum operations

Applied the method to quantum state preparation

Implemented a three-body quantum simulation experiment

Abstract

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.