Adiabatic Quantum Computing: An Overview

Quantum computations can be implemented not only by the action of quantum circuits, but by the adiabatic evolution of a system’s Hamiltonian. This can be done by initializing the system into the ground state of a simple Hamiltonian, and then adiabatically evolving the Hamiltonian to one whose ground state encodes the solution to the problem. The time complexity of the problem, or more basically, the speed at which the Hamiltonian can be evolved adiabatically, is related to the separation between the energy eigenvalues. In some cases, such as Grover Search, the standard computation complexity can be recovered. Importantly, any quantum circuit can be simulated adiabatically.