Digital adiabatic evolution is universally accurate.

Adiabatic evolution is a central paradigm in quantum physics. Digital simulations of adiabatic processes are generally regarded as resource-intensive, not only because of the long evolution time required, but also because algorithmic errors typically accumulate throughout the evolution, thereby demanding exceptionally deep circuits to preserve accuracy. This work demonstrates that digital adiabatic evolution is intrinsically accurate and robust to simulation errors. We analyze two Hamiltonian simulation methods-Trotterization and generalized quantum signal processing-and prove that the simulation error does not increase with time. We further show that accurate time-dependent adiabatic evolution can be achieved using only time-independent Hamiltonian-simulation algorithms. Numerical simulations of the adiabatic algorithms for molecular systems and linear equations confirm the theory, revealing that digital adiabatic evolution is substantially more efficient than previously assumed. Remarkably, our estimation for the first-order Trotterization error can be 10