Quantum Advantage: a Tensor Network Perspective

TL;DR

This paper reviews recent quantum advantage experiments, analyzing how tensor network methods have been used for classical simulation, highlighting their strengths, limitations, and implications for future quantum advantage research.

Contribution

It provides a comprehensive assessment of tensor network approaches in quantum advantage experiments, identifying current challenges and future directions for classical simulation methods.

Findings

Tensor network methods can simulate certain quantum advantage experiments efficiently.

Current tensor network approaches face limitations with increasing system complexity.

Future improvements in classical algorithms could challenge claims of quantum advantage.

Abstract

We review the recent quantum advantage experiments by IBM, D-Wave, and Google, focusing on cases where efficient classical simulations of the experiment were demonstrated or attempted using tensor network methods. We assess the strengths and limitations of these tensor network-based approaches and examine how the interplay between classical simulation and quantum hardware has advanced both fields. Our goal is to clarify what these results imply for the next generation of quantum advantage experiments. We identify regimes and system features that remain challenging for current tensor network approaches, and we outline directions where improved classical methods could further raise the standard for claiming quantum advantage. By analyzing this evolving competition, we aim to provide a clear view of where genuine, scalable quantum advantage is most likely to emerge.