Speaker
Description
Taking the continuum limit is essential for extracting physical observables from quantum simulations of lattice gauge theories. Achieving this limit requires careful control of all systematic uncertainties, including those from approximate time evolution. Existing methods for product formulas rely on complicated renormalization trajectories because of the dependence on both the lattice spacing and renormalized Trotter step-size. More fundamentally, no analogous method exists for the myriad other simulation algorithms, making systematic and fair cost comparisons impossible. This work addresses both problems. For product formulas, we show that Trotter errors are irrelevant operators that vanish in the continuum limit, allowing us to introduce a simplified renormalization trajectory independent of the Trotter step-size. To address the general case, we then present the Statistically-Bounded Time Evolution (SBTE) protocol, a new framework for applicable to any simulation algorithm. The central insight is that, since exact evolution introduces no UV divergences, approximation errors can be treated as a systematic uncertainty that must be driven below the working statistical uncertainty. This not only simplifies renormalization but, due to existing rigorous error bounds, provides an a priori guarantee that such errors do not affect the continuum limit. Ultimately, our protocol provides the first rigorous foundation for performing fair cost comparisons of taking the continuum limit between different simulation algorithms.