Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a non-unitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here we present a general algorithm for implementing the action of any non-unitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating non-unitary operations on intermediate-term and future quantum devices.
@article{arxiv.2106.12588,
title = {Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators},
author = {Anthony W. Schlimgen and Kade Head-Marsden and LeeAnn M. Sager and Prineha Narang and David A. Mazziotti},
journal= {arXiv preprint arXiv:2106.12588},
year = {2022}
}