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

TL;DR

This paper investigates the convergence of perturbative series in digitized quantum field theories, showing that certain digitizations can have finite convergence radii, and compares the resource efficiency of quantum computing methods for real-time evolution.

Contribution

It demonstrates that harmonic digitizations of lambda phi^4 models can have finite radius of convergence and compares quantum computing resource requirements for these models.

Findings

Harmonic digitizations improve convergence properties.

Finite radius of convergence for weak and strong coupling expansions.

Quantum computers may outperform classical methods for large systems.

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 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 $\lambda \phi^4$ 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 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.