Abstract:

The real time evolution of quantum field theory models can be calculated order by order in perturbation theory. For lambda phi^4 models, the perturbative series have a zero radius of convergence which motivated the design of digitized versions suitable for quantum computing. In agreement with general arguments suggesting that a large field cutoff affects convergence properties, we show that the harmonic digitizations of lambda 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 and universal quantum computers. Unless new approximate methods can be designed to calculate long perturbative series for large systems efficiently, it appears that digitization involving a few qubits per sites have the potential for more efficient calculations of the real-time evolution for large systems at intermediate  coupling.