Speaker
Description
Imaginary-time evolution (ITE) is a quantum primitive for ground-state preparation. Despite guaranteed asymptotic convergence, its runtime can be dominated by finite-time stagnation plateaus where energy gradients vanish, leaving the ground state fidelity small. We formalize this dynamical bottleneck, showing it creates an intrinsic false-convergence problem: gradient-based stopping criteria can signal success while the state remains far from the ground state. We derive bounds on stagnation duration and, under an edge-bulk isolation (EBI) spectral condition, explicitly map ground-gap spectral density to the stagnation-time tail, yielding the stagnation tail for random-matrix ensembles: level repulsion suppresses rare long stagnation events. We analytically demonstrate and numerically verify this relationship within the Random Transverse-Field Ising Model (RTFIM), an example of a typical many-body Hamiltonian. These results reveal that ITE's practical hardness can also be governed by how low-energy spectral structures control finite-time stagnation, rather than just its asymptotic convergence rate.
| Topic | Quantum algorithms for machine learning applications |
|---|---|
| Additional Topic | Theoretical foundations of quantum learning |