Perturbative boundaries of quantum advantage: Real-time evolution for digitized λϕ4 lattice models

Abstract

The real time evolution of quantum field theory models can be calculated order by order in perturbation theory. For $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ models, the perturbative series have a zero radius of convergence which in part motivated the design of digitized versions suitable for quantum computing. In agreement with general arguments suggesting that a large field cutoff modifies Dyson's reasoning and improves convergence properties, we show that the harmonic digitizations of $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ lattice field theories lead to weak coupling expansions with a finite radius of convergence. Similar convergence properties are found for strong coupling expansions. We compare the resources needed to calculate the real-time evolution of the digitized models with perturbative expansions to those needed to do so with universal quantum computers. Unless new approximate methods can be designed to calculate long perturbative series for large systems efficiently, it appears that the use of universal quantum computers with digitizations involving a few qubits per site has the potential for more efficient calculations of the real-time evolution for large systems at intermediate coupling.