Nonunitary Preparation of Nontrivial States from Trivial Regimes in Two-Dimensional Topological Insulators

While remarkable progress has been achieved in engineering nontrivial Hamiltonians across a wide range of physical platforms, preparing their corresponding nontrivial ground states remains a major experimental challenge. The commonly used strategy for state preparation relies on adiabatic protocols. However, when a trivial initial state is unitarily driven toward nontrivial regimes, the dynamics must cross gap-closing critical points, rendering the process intrinsically nonadiabatic, and the state remains topologically trivial. Here, we present a nonunitary method for dynamically preparing nontrivial states in two-dimensional topological insulators. By introducing dephasing noise into a slowly driven unitary evolution, we demonstrate that the topological number of the resulting dephased states can coincide with that of the target nontrivial Hamiltonian. This nearly adiabatic nonunitary state-preparation protocol provides a powerful alternative to conventional adiabatic approaches for accessing topological states.