When and for which observables quantum advantage will first emerge in QFT simulations

Determine the regimes and specific observables for which quantum computers will achieve a clear advantage over classical methods in quantum field theory simulations, particularly for real-time dynamics, strongly coupled systems, and finite-density settings. This entails identifying concrete problem classes and measurement targets where quantum devices outperform tensor networks, Monte Carlo, and other classical techniques, and specifying the conditions (models, parameters, circuit depths, and hardware capabilities) under which such advantage is realized.

Background

Throughout these lectures the authors analyze real-time and nonperturbative problems in 1+1D quantum field theories and benchmark quantum algorithms against classical tensor-network baselines. They emphasize that, while significant hardware demonstrations exist, a definitive quantum advantage has not yet been established for these tasks.

In the concluding chapter, the authors discuss future directions including higher-dimensional theories, PEPS limitations, fault tolerance, and improved state preparation. Against this backdrop they explicitly note that it is not yet known when quantum devices will surpass classical approaches and for which observables this will happen, especially in challenging regimes such as strong coupling, real-time evolution, and finite density.