Perturbative boundaries of quantum computing: real-time evolution for digitized $\lambda \phi^4$ lattice models

Robert Maxton; University of Iowa

We discuss the real-time evolution for $\lambda \phi^4$ lattice field theory. The zero radius of convergence of the corresponding perturbative series has motivated the development of a quantum computing algorithm for this problem. However, we show that the digitization of the problem is an approximation that significantly affects the convergence properties of weak and strong coupling expansions. In agreement with general arguments suggesting that a large field cutoff improves 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 or 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 sites have the potential for more efficient calculations of the real-time evolution for large systems at intermediate coupling.