Simulated annealing is a Monte-Carlo-based optimization method and inspired the development of quantum adiabatic computing based on the quantum adiabatic theorem. Quantum adiabatic computing is equivalent to the more standard circuit-based quantum computing. In both cases, entanglement is a critical quantum resource. However, it is unclear if high entanglement during a quantum protocol prohibits an efficient classical simulation/approximation.

I will discuss the variational ground-state quantum adiabatic theorem asserting that, under certain conditions, a time-dependent variational state prepared in the initial variational ground state and evolving according to a time-dependent variational principle remains close to the instantaneous variational ground state. Consequently, quantum adiabatic algorithms with classical ground states of the initial and final Hamiltonians admit (under the theorem’s assumptions) efficient classical simulation. I will demonstrate the approach in several examples.