Simulating a Neutral Atom Open Quantum System with Tensor Network States

There are many different computational frameworks that can simulate an open quantum system. In particular, tensor network states (TNS) excel for low-depth quantum circuits on a large number of sites. We model the density matrix of an open quantum system on a neutral atom array using different types of TNS, from matrix product operators (MPO) to matrix product density operators (MPDO). As the MPO by itself is not a faithful representation of a positive-definite matrix, we consider ways to improve its positivity without significantly increasing computation cost. To improve the performance of large tensor operations, we use a distributed-memory tensor contraction library, finding not only an improvement in wall time but also core-hour cost. Using this framework, we measure time evolution under the Transverse Field Ising Model (TFIM) to gauge the ability of a QAOA algorithm to optimize the TFIM through dissipation and dephasing noise. We also check the ability of an open quantum system to maintain accuracy under a randomly sampled circuit.