Simulating Neutral Atom Quantum Systems with Tensor Network States

TL;DR

This paper introduces a tensor network simulation method for neutral atom quantum systems with noise, including a new purity-preserving truncation, and investigates the robustness of quantum algorithms under various noise conditions.

Contribution

It presents a novel tensor network simulation technique with a purity-preserving truncation and applies it to study noise effects on quantum approximate optimization algorithms.

Findings

Large qubit circuits are more prone to failure under noise but maintain output robustness.

Optimized parameters are highly robust to noise, enabling pre-optimization on noisier systems.

Circuit performance varies with noise type, with some errors affecting results more than others.

Abstract

In this paper, we describe a tensor network simulation of a neutral atom quantum system under the presence of noise, while introducing a new purity-preserving truncation technique that compromises between the simplicity of the matrix product state and the positivity of the matrix product density operator. We apply this simulation to a near-optimized iteration of the quantum approximate optimization algorithm on a transverse field Ising model in order to investigate the influence of large system sizes on the performance of the algorithm. We find that while circuits with a large number of qubits fail more often under noise that depletes the qubit population, their outputs on a successful measurement are just as robust under Rydberg atom dissipation or qubit dephasing as smaller systems. However, such circuits might not perform as well under coherent multi-qubit errors such as Rydberg atom crosstalk. We also find that the optimized parameters are especially robust to noise, suggesting that a noisier quantum system can be used to find the optimal parameters before switching to a cleaner system for measurements of observables.