Error bounds for quantum formulas now include time-varying systems

Kaoru Mizuta, Tatsuhiko N. Ikeda, and Keisuke Fujii have established error bounds for Product Formulas (PFs) used in quantum simulation, extending their applicability to systems that change over time. Previously limited to time-independent systems, the researchers’ derivation now encompasses smooth time-dependent Hamiltonians using Floquet theory, originally designed for time-periodic systems, and maps time-dependent PF errors to those for time-independent PFs defined on an infinite-dimensional space. This work indicates “substantial error suppression in the system size,” offering “a much better estimate of gate counts” needed for quantum simulations and potentially accelerating algorithms for simulating materials and chemical reactions. This analytical approach maps the complexities of time-dependent PF errors onto those of their time-independent counterparts within an infinite-dimensional space, offering a novel pathway to improve simulation accuracy. The researchers’ derivation extends beyond standard PFs, proving applicable to a broader range of formulas including those used to model non-unitary dynamics. The team addressed the challenge of quantifying errors in two types of time-dependent PFs, standard and generalized formulas of varying orders, by using the principles of Floquet theory. This allowed them to translate the time evolution under time-dependent Hamiltonians into an equivalent process under a time-independent…